3892:
53:
6178:
6029:
6433:
6445:
2851:
1618:
2508:
2297:
2874:, which was constructed for precisely this purpose. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between quarks and antiquarks in a meson. However, the
3117:
that have not yet been definitively observed experimentally. A definitive observation of a glueball with the properties predicted by QCD would strongly confirm the theory. In principle, if glueballs could be definitively ruled out, this would be a serious experimental blow to QCD. But, as of 2013,
3677:
The basic notion "frustration" of the spin-glass is actually similar to the Wilson loop quantity of the QCD. The only difference is again that in the QCD one is dealing with SU(3) matrices, and that one is dealing with a "fluctuating" quantity. Energetically, perfect absence of frustration should be
2932:
or ChiPT, which is the QCD effective theory at low energies. More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u, d and s quark, which have small mass, it is still a good
955:
as a particle that could be separated and isolated, Gell-Mann often said that quarks were merely convenient mathematical constructs, not real particles. The meaning of this statement was usually clear in context: He meant quarks are confined, but he also was implying that the strong interactions
3417:
971:
The difference between
Feynman's and Gell-Mann's approaches reflected a deep split in the theoretical physics community. Feynman thought the quarks have a distribution of position or momentum, like any other particle, and he (correctly) believed that the diffusion of parton momentum explained
5297:
Gross, Franz; Klempt, Eberhard; Brodsky, Stanley J.; Buras, Andrzej J.; Burkert, Volker D.; Heinrich, Gudrun; Jakobs, Karl; Meyer, Curtis A.; Orginos, Kostas; Strickland, Michael; Stachel, Johanna; Zanderighi, Giulia; Brambilla, Nora; Braun-Munzinger, Peter; Britzger, Daniel (2023-12-12).
2911:, starts from the idea that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not. Until now, it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the
1386:
There are two different types of SU(3) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry that rotates different flavors of quarks to each other, or
1924:
1434:
2761:" of the hadrons The order of magnitude of the "bag radius" is 1 fm (= 10 m). Moreover, the above-mentioned stiffness is quantitatively related to the so-called "area law" behavior of the expectation value of the Wilson loop product
2139:
2923:
For specific problems, effective theories may be written down that give qualitatively correct results in certain limits. In the best of cases, these may then be obtained as systematic expansions in some parameters of the QCD Lagrangian. One such
1287:, namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances. Here, in contrast to Wegner, we have only the dual model, which is that one described in this article.
902:
wrote a preprint with a more detailed discussion of the additional quark quantum degree of freedom. This work was also presented by Albert
Tavkhelidze without obtaining consent of his collaborators for doing so at an international conference in
1406:
The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate
619:, a steady reduction in the strength of interactions between quarks and gluons as the energy scale of those interactions increases (and the corresponding length scale decreases). The asymptotic freedom of QCD was discovered in 1973 by
3878:
3678:
non-favorable and atypical for a spin glass, which means that one should add the loop product to the
Hamiltonian, by some kind of term representing a "punishment". In the QCD the Wilson loop is essential for the Lagrangian rightaway.
976:. Although Gell-Mann believed that certain quark charges could be localized, he was open to the possibility that the quarks themselves could not be localized because space and time break down. This was the more radical approach of
1398:
there are vacuum condensates of all the quarks whose mass is less than the QCD scale. This includes the up and down quarks, and to a lesser extent the strange quark, but not any of the others. The vacuum is symmetric under SU(2)
2866:. This approach uses a discrete set of spacetime points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation that is then carried out on
3262:
1025:), in which the carrier particles of a force can themselves radiate further carrier particles. (This is different from QED, where the photons that carry the electromagnetic force do not radiate further photons.)
3761:
There is also a correspondence between confinement in QCD â the fact that the color field is only different from zero in the interior of hadrons â and the behaviour of the usual magnetic field in the theory of
1279: distances. However, as already mentioned in the original paper of Franz Wegner, a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the
3249:
3681:
The relation between the QCD and "disordered magnetic systems" (the spin glasses belong to them) were additionally stressed in a paper by
Fradkin, Huberman and Shenker, which also stresses the notion of
3492:
3661:
3697:(force proportional to the length) of a rubber band. The non-abelian character of the SU(3) corresponds thereby to the non-trivial "chemical links", which glue different loop segments together, and "
645:
of an important global symmetry of quarks, detailed below, with the result of generating masses for hadrons far above the masses of the quarks, and making pseudoscalar mesons exceptionally light.
506:
1801:
2679:, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. This contrasts with
1075:. Since the force between color charges does not decrease with distance, it is believed that quarks and gluons can never be liberated from hadrons. This aspect of the theory is verified within
3745:
1295:
The color group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. The electric charge labels a representation of the local symmetry group U(1), which is gauged to give
2346:
5419:
2072:
1233:
on its direction of motion then it is called right-handed; otherwise, it is left-handed. Chirality and handedness are not the same, but become approximately equivalent at high energies.
649:
was awarded the 2008 Nobel Prize in
Physics for elucidating the phenomenon in 1960, a dozen years before the advent of QCD. Lattice simulations have confirmed all his generic predictions.
1391:. Flavor SU(3) is an approximate symmetry of the vacuum of QCD, and is not a fundamental symmetry at all. It is an accidental consequence of the small mass of the three lightest quarks.
4918:
2804:
872:
Three identical quarks cannot form an antisymmetric S-state. In order to realize an antisymmetric orbital S-state, it is necessary for the quark to have an additional quantum number.
2858:⟩ plot for static quarkâantiquark system held at a fixed separation, where blue is zero and red is the highest value (result of a lattice QCD simulation by M. Cardoso et al.)
2022:
1613:{\displaystyle {\mathcal {L}}_{\mathrm {QCD} }={\bar {\psi }}_{i}\left(i\gamma ^{\mu }(D_{\mu })_{ij}-m\,\delta _{ij}\right)\psi _{j}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu }}
1403:
rotations of up and down, and to a lesser extent under rotations of up, down, and strange, or full flavor group SU(3), and the observed particles make isospin and SU(3) multiplets.
2661:
4946:
Cardoso, M.; et al. (2010). "Lattice QCD computation of the colour fields for the static hybrid quarkâgluonâantiquark system, and microscopic study of the
Casimir scaling".
2292:{\displaystyle G_{\mu \nu }^{a}=\partial _{\mu }{\mathcal {A}}_{\nu }^{a}-\partial _{\nu }{\mathcal {A}}_{\mu }^{a}+gf^{abc}{\mathcal {A}}_{\mu }^{b}{\mathcal {A}}_{\nu }^{c}\,,}
4562:(Dedicated to the 40th Anniversary of the Discovery of the Quantum Number Color). Report presented at the 99th Session of the JINR Scientific Council, Dubna, 19â20 January 2006.
2115:
6063:
1659:
68:
3173:
3086:
Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the running of the QCD coupling as probed through
2728:
680:, in which he related that he had been influenced by Joyce's words: "The allusion to three quarks seemed perfect." (Originally, only three quarks had been discovered.)
5459:
3118:
scientists are unable to confirm or deny the existence of glueballs definitively, despite the fact that particle accelerators have sufficient energy to generate them.
1778:
499:
3531:
2836:
to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date.
1973:
609:, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although analytically unproven, color confinement is well established from
4412:
Gell-Mann, M. (1961). "The
Eightfold Way: A Theory of strong interaction symmetry" (No. TID-12608; CTSL-20). California Inst. of Tech., Pasadena. Synchrotron Lab (
6713:
6207:
1945:
146:
3784:
3537:, are "frozen" to fixed values (quenching). In contrast, in the QCD they "fluctuate" (annealing), and through the large number of gauge degrees of freedom the
2818:
Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below.
6483:
6315:
5882:
5692:
2406:
2386:
1751:
1731:
1711:
1691:
5774:
5733:
2933:
approximate symmetry. Depending on the number of quarks that are treated as light, one uses either SU(2) ChiPT or SU(3) ChiPT. Other effective theories are
2495:). In lattice QCD, the final term of the above Lagrangian is discretized via Wilson loops, and more generally the behavior of Wilson loops can distinguish
6802:
492:
4803:
Perhaps one can guess that in the "original" model mainly the quarks would fluctuate, whereas in the present one, the "dual" model, mainly the gluons do.
937:
5393:
890:. The problem considered in this preprint was suggested by Nikolay Bogolyubov, who advised Boris Struminsky in this research. In the beginning of 1965,
6192:
3412:{\displaystyle (\,s_{i}\to s_{i}\cdot \epsilon _{i}\quad \,J_{i,k}\to \epsilon _{i}J_{i,k}\epsilon _{k}\,\quad s_{k}\to s_{k}\cdot \epsilon _{k}\,)\,.}
142:
5512:
2878:
makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars).
6056:
2833:
1120:
1045:
6681:
5537:
2730:), which represents some kind of "stiffness" of the interaction between the particle and its anti-particle at large distances, similar to the
5641:
4054:
3891:
951:
Since free quark searches consistently failed to turn up any evidence for the new particles, and because an elementary particle back then was
6310:
5872:
5287:
5268:
5238:
4229:
4086:
2612:
5764:
5452:
3551:
the thermodynamics of the Mattis spin glass corresponds in fact simply to a "ferromagnet in disguise", just because these systems have no "
1160:
4260:
1044:
allowed physicists to make precise predictions of the results of many high energy experiments using the quantum field theory technique of
5620:
968:(since they were parts of hadrons). By particles, Feynman meant objects that travel along paths, elementary particles in a field theory.
6393:
5502:
4192:
605:. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quarkâantiquark pair is
4788:
6049:
2511:
The pattern of strong charges for the three colors of quark, three antiquarks, and eight gluons (with two of zero charge overlapping).
6449:
703:. Other than this nomenclature, the quantum parameter "color" is completely unrelated to the everyday, familiar phenomenon of color.
6476:
6217:
6032:
5712:
3182:
2703:
Detailed computations with the above-mentioned
Lagrangian show that the effective potential between a quark and its anti-quark in a
172:
1283:, e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!)
1252:
symmetries are those in which one transformation is applied on left-handed particles and the inverse on the right-handed particles.
4078:
6398:
5962:
5769:
5532:
69:
5565:
3558:
3422:
812:
6823:
5922:
5825:
5805:
5445:
4331:
4288:
3997:
2938:
758:
6629:
6358:
5728:
5487:
5482:
4778:
800:
1919:{\displaystyle \left(D_{\mu }\right)_{ij}=\partial _{\mu }\delta _{ij}-ig\left(T_{a}\right)_{ij}{\mathcal {A}}_{\mu }^{a}\,}
6828:
6249:
6197:
4044:
1345:
642:
468:
116:
72:
67:
5877:
4012:
3259:
quantities can independently and "randomly" take the values ±1, which corresponds to a most-simple gauge transformation
2942:
2618:
of SU(3). They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the
6469:
6408:
6001:
5527:
4542:
A. Tavkhelidze. Proc. Seminar on High Energy
Physics and Elementary Particles, Trieste, 1965, Vienna IAEA, 1965, p. 763.
4002:
2934:
754:
353:
3704:
3693:, where, analogously to Wilson loops, so-called "entangled nets" appear, which are important for the formation of the
3683:
3098:
of hadrons and their weak matrix elements are promising candidates for future quantitative tests. The whole subject of
1271:
1013:, together with physicist Murray Gell-Mann. In particular, they employed the general field theory developed in 1954 by
606:
6766:
5996:
5790:
3754:
is a characteristic correlation length for the glued loops, corresponding to the above-mentioned "bag radius", while λ
2118:
1230:
73:
70:
5570:
3758:
is the wavelength of an excitation) any non-trivial correlation vanishes totally, as if the system had crystallized.
62:
2305:
80:
71:
6597:
6570:
3555:" at all. This term is a basic measure in spin glass theory. Quantitatively it is identical with the loop product
2976:
2964:
2929:
2537:
2027:
1796:
1781:
1662:
1084:
834:
78:
63:
5738:
6363:
4022:
3042:
3009:
2628:
Each type of quark has a corresponding antiquark, of which the charge is exactly opposite. They transform in the
2597:
1420:
1080:
987:
964:
865:
79:
1269:â there is practically no interaction between the particles. This is in contrast â more precisely one would say
6703:
6368:
5974:
4695:
3127:
2629:
1018:
815:). To gain greater insight, the hadrons were sorted into groups having similar properties and masses using the
638:
564:
433:
363:
60:
6282:
5846:
5671:
5646:
5099:
Vannimenus, J.; Toulouse, G. (1977). "Theory of the frustration effect. II. Ising spins on a square lattice".
4741:
Wegner, F. (1971). "Duality in
Generalized Ising Models and Phase Transitions without Local Order Parameter".
3966:
2688:
57:
4884:
2775:
2482:
correspond to the quark mass and coupling of the theory, respectively, which are subject to renormalization.
6437:
6150:
6140:
5702:
5585:
5252:
5228:
4555:
4486:
Fyodor Tkachov (2009). "A contribution to the history of quarks: Boris Struminsky's 1965 JINR publication".
4151:
4108:
4039:
3552:
3073:
2680:
2130:
1978:
1296:
1246:
symmetries (also called diagonal symmetries) mean the same transformation is applied on the two chiralities.
817:
688:
580:
134:
4878:
4032:
3943:
3103:
2635:
1214:
Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate
1148:
1096:
833:, went on to propose in 1963 that the structure of the groups could be explained by the existence of three
61:
6787:
6649:
6155:
6013:
5937:
5932:
5867:
5795:
5697:
5600:
5575:
5492:
5184:
Bergmann, A.; Owen, A. (2004). "Dielectric relaxation spectroscopy of poly (PHD) during crystallization".
4663:
4572:
Greenberg, O. W. (1964). "Spin and Unitary Spin Independence in a Paraquark Model of Baryons and Mesons".
4027:
3763:
3067:
2925:
2875:
2353:
2122:
632:
383:
268:
208:
5748:
5651:
5615:
5560:
4049:
3055:
2941:(which expands around large ratios of energy scales). In addition to effective theories, models like the
2419:
of SU(3) (the generators of the adjoint representation). Note that the rules to move-up or pull-down the
1200:
1022:
58:
6792:
6761:
6624:
6545:
6403:
6277:
6244:
5986:
5981:
5820:
5815:
5605:
2084:
1204:
931:
780:
568:
258:
3094:. Other non-perturbative tests are currently at the level of 5% at best. Continuing work on masses and
5350:
5000:
65:
6751:
6575:
6535:
6353:
6292:
6287:
6261:
6108:
5927:
5661:
5497:
5468:
5365:
5150:
5108:
5073:
5022:
4965:
4929:
4832:
4750:
4713:
4655:
4620:
4581:
4468:
4437:
4379:
4340:
4297:
4160:
4117:
3971:
3958:
3090:
computations of heavy-quarkonium spectra. There is a recent claim about the mass of the heavy meson B
2672:
983:
560:
168:
108:
31:
4668:
3781:
of quantum chromodynamics. Mathematically, this correspondendence is supported by the second term,
2979:
was prompted by the necessity of explaining the properties of hadrons during the development of the
1627:
1170:
is based on certain symmetries of nature whose existence is deduced from observations. These can be
56:
6726:
6585:
6580:
6565:
6540:
6517:
6493:
6320:
5991:
5957:
5892:
5810:
5800:
5595:
5403:
3141:
2416:
1670:
1311:
1222:
940:, later called color charge. Han and Nambu noted that quarks might interact via an octet of vector
520:
443:
403:
218:
203:
86:
4646:
Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). "Advantages of the color octet gluon picture".
2810:
enclosed by the loop. For this behavior the non-abelian behavior of the gauge group is essential.
1195:, which are symmetries whose operations must be simultaneously applied to all points of spacetime.
74:
6782:
6659:
6654:
6607:
6348:
6118:
5625:
5311:
5135:
5046:
5012:
4981:
4955:
4848:
4822:
4522:
4487:
4395:
3913:
3698:
2075:
1029:
1010:
919:
899:
891:
887:
808:
715:
616:
532:
293:
64:
4813:
M. EidemĂŒller; H.G. Dosch; M. Jamin (2000). "The field strength correlator from QCD sum rules".
4368:
Gell-Mann, M (1956). "The Interpretation of the New Particles as Displaced Charged Multiplets".
1375:(1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an
378:
4786:
4256:
2710:
2707:
contains a term that increases in proportion to the distance between the quark and anti-quark (
77:
6797:
6746:
6691:
6671:
6557:
6234:
5676:
5329:
5283:
5264:
5234:
5166:
5038:
4774:
4225:
4082:
3962:
3933:
3419:
This means that thermodynamic expectation values of measurable quantities, e.g. of the energy
3095:
3032:
2571:
2496:
2492:
1975:
in the fundamental representation. An explicit representation of these generators is given by
1756:
1376:
1364:
1127:
1072:
841:. Gell-Mann also briefly discussed a field theory model in which quarks interact with gluons.
796:
602:
428:
358:
323:
253:
248:
213:
188:
164:
160:
4188:
3503:
1950:
1371:(1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry U
75:
59:
6736:
6676:
6602:
6413:
6160:
6145:
6086:
5947:
5373:
5321:
5299:
5193:
5158:
5116:
5081:
5030:
4973:
4840:
4758:
4721:
4673:
4628:
4608:
4589:
4525:, B. Struminsky, A. Tavkhelidze. On composite models in the theory of elementary particles.
4445:
4387:
4370:
4348:
4305:
4213:
4168:
4125:
3992:
3767:
3131:
2827:
2468:
1167:
1088:
1057:
1056:
in 1979. These experiments became more and more precise, culminating in the verification of
895:
849:
822:
804:
784:
772:
684:
666:
in its present sense. It originally comes from the phrase "Three quarks for Muster Mark" in
659:
588:
413:
408:
308:
283:
243:
100:
44:
3873:{\displaystyle \propto gG_{\mu }^{a}{\bar {\psi }}_{i}\gamma ^{\mu }T_{ij}^{a}\psi _{j}\,,}
998:
in 1969. This led physicists to abandon the S-matrix approach for the strong interactions.
76:
66:
6756:
6666:
6612:
6512:
6335:
6202:
5969:
5707:
5656:
5432:
4792:
4704:
4559:
4428:
3690:
3667:. However, for a Mattis spin glass â in contrast to "genuine" spin glasses â the quantity
3038:
3017:
2692:
2676:
1424:
1192:
1152:
1049:
1006:
977:
959:
726:
458:
343:
333:
328:
318:
278:
273:
233:
120:
3109:
One qualitative prediction of QCD is that there exist composite particles made solely of
1929:
473:
5369:
5154:
5112:
5077:
5026:
4969:
4836:
4754:
4717:
4659:
4624:
4585:
4472:
4441:
4383:
4344:
4301:
4164:
4121:
6686:
6641:
6619:
6507:
6373:
6072:
5912:
5887:
5666:
5257:
5248:
4691:
3908:
3897:
3694:
3061:
2867:
2731:
2391:
2371:
1785:
1736:
1716:
1696:
1676:
1226:
1174:
1136:
1037:
1014:
927:
845:
830:
764:
668:
646:
628:
584:
398:
368:
313:
303:
288:
198:
104:
40:
5325:
5120:
4844:
4449:
3701:" means in the polymer analogy simply the fact that in the short-wave limit, i.e. for
3008:
The first evidence for quarks as real constituent elements of hadrons was obtained in
1275:â to what one is used to, since usually one connects the absence of interactions with
17:
6817:
6343:
6302:
6008:
5942:
5917:
5517:
5085:
4985:
4677:
4413:
4399:
3987:
2967:
one can derive sets of relations that connect different observables with each other.
2958:
2897:
2891:
2619:
2579:
1789:
1300:
1041:
1005:
as the source of a "strong field" was developed into the theory of QCD by physicists
962:
argued that high energy experiments showed quarks are real particles: he called them
923:
857:
792:
768:
730:
719:
624:
576:
418:
373:
338:
193:
5050:
4852:
4244:
3106:
is a non-perturbative test bed for QCD that still remains to be properly exploited.
6721:
6325:
6256:
6165:
6123:
6113:
5952:
5862:
5580:
5522:
5507:
4007:
3953:
3099:
3047:
2946:
2608:
2575:
2529:
1208:
1182:
1132:
1002:
934:
911:
853:
826:
700:
692:
478:
448:
423:
393:
263:
238:
223:
112:
1151:
should be formed at high temperature and density. What are the properties of this
930:
independently resolved the problem by proposing that quarks possess an additional
5214:'s braid group, which is nonabelian, since one braid can wind around another one.
6239:
6133:
6101:
6096:
5610:
5429:
4173:
4146:
4130:
4103:
3982:
3087:
2980:
2863:
2845:
2593:
2544:
2533:
2487:
2349:
1419:
The dynamics of the quarks and gluons are defined by the quantum chromodynamics
1186:
1076:
1033:
941:
673:
620:
610:
453:
438:
388:
348:
298:
5034:
4977:
4593:
1221:
There are additional global symmetries whose definitions require the notion of
6741:
6731:
5389:
5211:
4632:
3938:
3887:
3135:
1395:
1349:
1240:
symmetries involve independent transformations of these two types of particle.
1143:
1092:
463:
228:
5333:
5162:
5042:
6592:
6461:
5743:
4221:
2850:
2758:
1380:
1178:
4726:
4699:
1139:. How does QCD give rise to the physics of nuclei and nuclear constituents?
860:
with parallel spins (this situation was peculiar, because since quarks are
676:. On June 27, 1978, Gell-Mann wrote a private letter to the editor of the
6418:
5841:
5437:
3114:
3051:
1788:
connecting the spinor representation to the vector representation of the
991:
915:
5064:
Mattis, D. C. (1976). "Solvable Spin Systems with Random Interactions".
6091:
5259:
Quarks & Leptons: An Introductory Course in Modern Particle Physics
5017:
4827:
4391:
4353:
4326:
4310:
4283:
3538:
2912:
2862:
Among non-perturbative approaches to QCD, the most well established is
2747:
2525:
1408:
1400:
973:
904:
861:
788:
745:, "color") is applied to the theory of color charge, "chromodynamics".
552:
5424:
5377:
5170:
4762:
6696:
3928:
2735:
2684:
776:
548:
544:
5197:
579:
of the theory, just as photons are for the electromagnetic force in
5316:
3689:
A further analogy consists in the already mentioned similarity to
1177:, which are the symmetries that act independently at each point in
1111:
779:. It seemed that such a large number of particles could not all be
5411:
5398:
4960:
4530:
4509:
B. V. Struminsky, Magnetic moments of baryons in the quark model.
4492:
3923:
3918:
3110:
3021:
2871:
2849:
2743:
2704:
2604:
2547:
2506:
1666:
1053:
945:
877:
B. V. Struminsky, Magnetic moments of barions in the quark model,
844:
Perhaps the first remark that quarks should possess an additional
838:
696:
540:
536:
6041:
4552:
986:
proposed that pointlike partons would imply certain relations in
4881:
only at extremely large pressures and/or temperatures, e.g. for
4526:
4510:
4426:
M. Gell-Mann (1964). "A Schematic Model of Baryons and Mesons".
3013:
1065:
995:
878:
556:
6465:
6045:
5441:
4865:
See all standard textbooks on the QCD, e.g., those noted above
2532:
whose gauging is the content of QCD. Quarks are represented by
956:
could probably not be fully described by quantum field theory.
775:
discovered a large and ever-growing number of particles called
4513:-Preprint P-1939, Dubna, Russia. Submitted on January 7, 1965.
3244:{\displaystyle J_{i,k}=\epsilon _{i}\,J_{0}\,\epsilon _{k}\,.}
3077:
2507:
1661:
is the quark field, a dynamical function of spacetime, in the
1087:
requires a claimant to produce such a proof. Other aspects of
1061:
5300:"50 Years of quantum chromodynamics: Introduction and Review"
4700:"Conservation of Isotopic Spin and Isotopic Gauge Invariance"
740:
734:
3428:
3179: =1,...,N, with the special fixed "random" couplings
2983:. The notion of color was necessitated by the puzzle of the
2683:, in which only the first kind of interaction occurs, since
2312:
2269:
2250:
2209:
2177:
1899:
1441:
631:
in the same year. For this work, all three shared the 2004
51:
3487:{\textstyle {\mathcal {H}}:=-\sum s_{i}\,J_{i,k}\,s_{k}\,,}
3138:, which are systems with the usual spin degrees of freedom
3027:
Several good quantitative tests of perturbative QCD exist:
2937:(which expands around heavy quark mass near infinity), and
2832:
This approach is based on asymptotic freedom, which allows
1947:
to the gluon fields via the infinitesimal SU(3) generators
1079:
computations, but is not mathematically proven. One of the
3656:{\displaystyle P_{W}:\,=\,J_{i,k}J_{k,l}...J_{n,m}J_{m,i}}
2578:
doublets. They carry global quantum numbers including the
543:. Quarks are fundamental particles that make up composite
3766:: there the magnetism is confined to the interior of the
1218:, which is broken by the differing masses of the quarks.
571:. The QCD analog of electric charge is a property called
5227:
Greiner, Walter; Schramm, Stefan; Stein, Eckart (2007).
5210:
Mathematically, the flux-line lattices are described by
4551:
V. A. Matveev and A. N. Tavkhelidze (INR, RAS, Moscow)
4147:"Reliable perturbative results for strong interactions"
3774:
of that theory is analogous to the confinement radius
2768:
of the ordered coupling constants around a closed loop
1265:
means that at large energy â this corresponds also to
1225:, discrimination between left and right-handed. If the
5384:
5338:
A highly technical review with almost 5000 references.
3425:
2742: of the quarks to the interior of hadrons, i.e.
4887:
3787:
3707:
3561:
3506:
3265:
3185:
3144:
2778:
2713:
2638:
2394:
2374:
2308:
2142:
2087:
2030:
1981:
1953:
1932:
1804:
1759:
1739:
1719:
1699:
1679:
1630:
1437:
881:-Preprint P-1939, Dubna, Submitted on January 7, 1965
4104:"Ultraviolet behavior of non-abelian gauge theories"
1310:
flavors of massless quarks, then there is a global (
6775:
6712:
6640:
6556:
6528:
6500:
6386:
6334:
6301:
6270:
6227:
6216:
6185:
6079:
5905:
5855:
5834:
5783:
5757:
5721:
5685:
5634:
5553:
5546:
5475:
4932:. (July 1979). The bag model of quark confinement.
994:and protons, which were verified in experiments at
5256:
4912:
4771:Lattice Gauge Theories and Monte Carlo Simulations
3872:
3739:
3655:
3525:
3486:
3411:
3243:
3167:
2798:
2722:
2655:
2400:
2380:
2340:
2291:
2109:
2066:
2016:
1967:
1939:
1918:
1772:
1745:
1725:
1705:
1685:
1653:
1612:
5407:The Weight of the World Is Quantum Chromodynamics
3740:{\displaystyle 0\leftarrow \lambda _{w}\ll R_{c}}
2949:are often used when discussing general features.
2550:. They also carry electric charge (either −
1926:couples the quark field with a coupling strength
4609:"Three-Triplet Model with Double SU(3) Symmetry"
4553:The quantum number color, colored quarks and QCD
848:was made as a short footnote in the preprint of
4773:. Singapore: World Scientific. pp. 60â73.
870:
725:Since the theory of electric charge is dubbed "
55:
6208:Mathematical formulation of the Standard Model
5415:Quantum chromodynamics with advanced computing
5399:Ab Initio Determination of Light Hadron Masses
2341:{\displaystyle {\mathcal {A}}_{\mu }^{a}(x)\,}
914:; in the quark model, it is composed of three
6477:
6057:
5453:
5136:"Gauge symmetries in random magnetic systems"
4505:
4503:
3001:. This has been dealt with in the section on
2067:{\displaystyle \lambda _{a}\,(a=1\ldots 8)\,}
837:of smaller particles inside the hadrons: the
500:
8:
2793:
2780:
910:A similar mysterious situation was with the
4327:"Charge Independence Theory of V Particles"
3122:Cross-relations to condensed matter physics
2352:, dynamical functions of spacetime, in the
6484:
6470:
6462:
6224:
6064:
6050:
6042:
5550:
5460:
5446:
5438:
5001:"Experimental tests of asymptotic freedom"
4075:An introduction to the confinement problem
1131:: the equations of QCD remain unsolved at
783:. First, the particles were classified by
507:
493:
36:
30:"QCD" redirects here. For other uses, see
5315:
5101:Journal of Physics C: Solid State Physics
5016:
4959:
4904:
4886:
4826:
4725:
4667:
4491:
4352:
4309:
4172:
4129:
3866:
3860:
3850:
3842:
3832:
3822:
3811:
3810:
3803:
3798:
3786:
3731:
3718:
3706:
3641:
3625:
3600:
3584:
3579:
3575:
3566:
3560:
3511:
3505:
3480:
3474:
3469:
3457:
3452:
3446:
3427:
3426:
3424:
3405:
3401:
3395:
3382:
3369:
3363:
3357:
3341:
3331:
3312:
3307:
3300:
3287:
3274:
3269:
3264:
3237:
3231:
3226:
3220:
3215:
3209:
3190:
3184:
3164:
3149:
3143:
3134:forms the basis of the well-known Mattis
2787:
2779:
2777:
2712:
2642:
2640:
2639:
2637:
2393:
2373:
2337:
2322:
2317:
2311:
2310:
2307:
2285:
2279:
2274:
2268:
2267:
2260:
2255:
2249:
2248:
2235:
2219:
2214:
2208:
2207:
2200:
2187:
2182:
2176:
2175:
2168:
2155:
2147:
2141:
2106:
2100:
2092:
2086:
2063:
2041:
2035:
2029:
2013:
2005:
1999:
1986:
1980:
1964:
1958:
1952:
1936:
1931:
1915:
1909:
1904:
1898:
1897:
1887:
1877:
1850:
1840:
1824:
1814:
1803:
1764:
1758:
1738:
1718:
1698:
1678:
1650:
1635:
1629:
1601:
1596:
1586:
1578:
1564:
1555:
1537:
1532:
1517:
1507:
1494:
1476:
1465:
1464:
1447:
1446:
1440:
1439:
1436:
1303:. If one considers a version of QCD with
1185:and requires the introduction of its own
864:, such a combination is forbidden by the
706:The force between quarks is known as the
695:" by loose analogy to the three kinds of
583:. The theory is an important part of the
27:Theory of the strong nuclear interactions
5005:Progress in Particle and Nuclear Physics
3126:There are unexpected cross-relations to
3016:. The first evidence for gluons came in
2485:An important theoretical concept is the
1071:The other side of asymptotic freedom is
613:calculations and decades of experiments.
4913:{\displaystyle T\approx 5\cdot 10^{12}}
4065:
2896:A well-known approximation scheme, the
2799:{\displaystyle \,\langle P_{W}\rangle }
1181:. Each such symmetry is the basis of a
1048:. Evidence of gluons was discovered in
598:QCD exhibits three salient properties:
592:
39:
6682:Atomic, molecular, and optical physics
5538:Two-dimensional conformal field theory
2691:must be considered too (except in the
2017:{\displaystyle T_{a}=\lambda _{a}/2\,}
1199:QCD is a non-abelian gauge theory (or
1147:: the equations of QCD predict that a
886:Boris Struminsky was a PhD student of
5430:Cern Courier, The history of QCD with
4821:(1â3). Heidelberg, Germany: 421â425.
4284:"Charge Independence for V-particles"
3770:, i.e., the London penetration depth
3541:plays an important role (see below).
3533:, which in the QCD correspond to the
2656:{\displaystyle {\bar {\mathbf {3} }}}
2356:of the SU(3) gauge group, indexed by
2123:electromagnetic field strength tensor
1383:are closely related to this anomaly.
1149:plasma (or soup) of quarks and gluons
1091:QCD are the exploration of phases of
821:, invented in 1961 by Gell-Mann and
7:
6444:
1379:. Gluon field configurations called
829:, correcting an earlier approach of
691:or QED) are usually referred to as "
3082:Heavy-quark production in colliders
2687:have no charge. Diagrams involving
1207:gauge group obtained by taking the
1161:(more unsolved problems in physics)
4463:M. Gell-Mann; H. Fritzsch (2010).
2197:
2165:
2110:{\displaystyle G_{\mu \nu }^{a}\,}
1837:
1454:
1451:
1448:
595:has been gathered over the years.
25:
6033:Template:Quantum mechanics topics
4465:Murray Gell-Mann: Selected Papers
4189:"The Nobel Prize in Physics 2004"
4055:YangâMills existence and mass gap
3880:on the r.h.s. of the Lagrangian.
3035:as deduced from many observations
1060:at the level of a few percent at
918:with parallel spins. In 1964â65,
799:; then, in 1953â56, according to
173:Physics beyond the Standard Model
6443:
6432:
6431:
6176:
6028:
6027:
5420:Standard model gets right answer
4282:Nakano, T; Nishijima, N (1953).
3890:
2738:band (see below). This leads to
2643:
2463:indices one has the non-trivial
6803:Timeline of physics discoveries
5326:10.1140/epjc/s10052-023-11949-2
5304:The European Physical Journal C
5233:. Berlin Heidelberg: Springer.
4332:Progress of Theoretical Physics
4289:Progress of Theoretical Physics
4263:from the original on 2007-08-20
4195:from the original on 2010-11-06
4102:D.J. Gross; F. Wilczek (1973).
3998:Soft-collinear effective theory
3364:
3306:
3064:produced in hadronic collisions
2939:soft-collinear effective theory
2117:represents the gauge invariant
759:History of quantum field theory
6359:Causal dynamical triangulation
5282:. Cambridge University Press.
4607:Han, M. Y.; Nambu, Y. (1965).
3816:
3711:
3402:
3375:
3324:
3280:
3266:
2647:
2625:of all these symmetry groups.
2334:
2328:
2060:
2042:
1654:{\displaystyle \psi _{i}(x)\,}
1647:
1641:
1514:
1500:
1470:
1032:in the strong interactions by
1:
6198:Spontaneous symmetry breaking
4845:10.1016/S0920-5632(00)00598-3
4450:10.1016/S0031-9163(64)92001-3
4045:Symmetry in quantum mechanics
3168:{\displaystyle s_{i}=\pm 1\,}
3130:. For example, the notion of
3041:in polarized and unpolarized
1229:of a particle has a positive
718:, and is responsible for the
687:in QCD (as opposed to one in
643:spontaneous symmetry breaking
593:experimental evidence for QCD
117:Spontaneous symmetry breaking
5086:10.1016/0375-9601(76)90396-0
4769:Rebbi, Claudio, ed. (1983).
4678:10.1016/0370-2693(73)90625-4
4003:Heavy quark effective theory
3002:
2935:heavy quark effective theory
2757:, corresponding to former "
1344:(1). The chiral symmetry is
1211:to define a local symmetry.
755:History of quantum mechanics
741:
6767:Quantum information science
5997:Quantum information science
5280:Quarks, Gluons and Lattices
5121:10.1088/0022-3719/10/18/008
4174:10.1103/PhysRevLett.30.1346
4131:10.1103/PhysRevLett.30.1343
3768:Abrikosov flux-line lattice
3499:coupling degrees of freedom
3033:running of the QCD coupling
2467:rules corresponding to the
2119:gluon field strength tensor
1363:) with the formation of a
1257:Additional remarks: duality
1114:Unsolved problem in physics
813:Gell-MannâNishijima formula
771:in the 1950s, experimental
6845:
6598:Classical electromagnetism
5035:10.1016/j.ppnp.2006.06.001
4978:10.1103/PhysRevD.81.034504
4594:10.1103/PhysRevLett.13.598
2965:Operator product expansion
2956:
2930:chiral perturbation theory
2889:
2843:
2825:
2671:According to the rules of
2538:fundamental representation
1797:gauge covariant derivative
1782:gauge covariant derivative
1663:fundamental representation
1314:) flavor symmetry group SU
1085:Clay Mathematics Institute
752:
735:
147:Standard Model mathematics
29:
6427:
6364:Canonical quantum gravity
6174:
6022:
5433:Prof. Dr. Harald Fritzsch
5263:. John Wiley & Sons.
5134:Fradkin, Eduardo (1978).
4999:Bethke, S. (2007-04-01).
4815:Nucl. Phys. B Proc. Suppl
4633:10.1103/PhysRev.139.B1006
4023:Deep inelastic scattering
3974:â a more general category
3043:deep inelastic scattering
3010:deep inelastic scattering
2723:{\displaystyle \propto r}
1409:string description of QCD
1081:Millennium Prize Problems
988:deep inelastic scattering
866:Pauli exclusion principle
852:in connection with the Ω
678:Oxford English Dictionary
6704:Condensed matter physics
6369:Superfluid vacuum theory
5278:Creutz, Michael (1985).
5163:10.1103/physrevb.18.4789
4920: K or larger.
4218:The Quark and the Jaguar
4013:NambuâJona-Lasinio model
3674:never becomes negative.
3128:condensed matter physics
2943:NambuâJona-Lasinio model
2699:Area law and confinement
2630:conjugate representation
2611:, since they lie in the
2515:Quarks are massive spin-
1773:{\displaystyle D_{\mu }}
1367:. The vector symmetry, U
1135:relevant for describing
856:being composed of three
639:Chiral symmetry breaking
565:non-abelian gauge theory
6151:Quantum electrodynamics
6141:Electroweak interaction
5693:2D free massless scalar
5586:Quantum electrodynamics
5513:QFT in curved spacetime
4152:Physical Review Letters
4109:Physical Review Letters
4040:Quantum electrodynamics
3764:type-II superconductors
3526:{\displaystyle J_{i,k}}
3074:Event shape observables
2806:is proportional to the
2499:and deconfined phases.
2435:, (+, ..., +), so that
2131:quantum electrodynamics
1968:{\displaystyle T_{a}\,}
1001:In 1973 the concept of
689:quantum electrodynamics
627:, and independently by
581:quantum electrodynamics
135:Electroweak interaction
6824:Quantum chromodynamics
6788:Nobel Prize in Physics
6650:Relativistic mechanics
6129:Quantum chromodynamics
6014:Quantum thermodynamics
5938:On shell and off shell
5933:Loop quantum cosmology
5775:N = 4 super YangâMills
5734:N = 1 super YangâMills
5601:Scalar electrodynamics
5591:Quantum chromodynamics
5493:Conformal field theory
5469:Quantum field theories
5425:Quantum Chromodynamics
5349:Frank Wilczek (2000).
5230:Quantum Chromodynamics
4914:
4727:10.1103/PhysRev.96.191
4145:H.D. Politzer (1973).
4028:Jet (particle physics)
3874:
3741:
3657:
3527:
3488:
3413:
3245:
3169:
2926:effective field theory
2876:numerical sign problem
2859:
2800:
2724:
2657:
2620:singlet representation
2613:adjoint representation
2598:flavor quantum numbers
2512:
2402:
2382:
2354:adjoint representation
2342:
2293:
2111:
2068:
2018:
1969:
1941:
1920:
1774:
1747:
1727:
1707:
1687:
1655:
1614:
1352:to the vector (L+R) SU
1166:Every field theory of
974:diffractive scattering
907:(Italy), in May 1965.
884:
763:With the invention of
699:(red, green and blue)
633:Nobel Prize in Physics
607:spontaneously produced
567:, with symmetry group
531:) is the study of the
525:quantum chromodynamics
139:Quantum chromodynamics
83:
18:Quantum Chromodynamics
6793:Philosophy of physics
6245:Cosmological constant
5987:Quantum hydrodynamics
5982:Quantum hadrodynamics
5606:Scalar chromodynamics
5186:Polymer International
4915:
4325:Nishijima, K (1955).
4073:J. Greensite (2011).
3875:
3742:
3658:
3528:
3489:
3414:
3246:
3170:
2853:
2801:
2750:, with typical radii
2725:
2675:, and the associated
2658:
2570:) and participate in
2510:
2403:
2383:
2343:
2294:
2112:
2069:
2019:
1970:
1942:
1921:
1775:
1748:
1728:
1708:
1688:
1656:
1615:
169:Neutrino oscillations
89:of the Standard Model
82:
6829:Quantum field theory
6752:Mathematical physics
6354:Loop quantum gravity
6293:Theory of everything
6288:Grand Unified Theory
6262:Neutrino oscillation
6109:Quantum field theory
5958:Quantum fluctuations
5928:Loop quantum gravity
5498:Lattice field theory
5390:The millennium prize
4930:Kenneth Alan Johnson
4885:
4467:. World Scientific.
4272:retrieved 6 May 2017
3972:Quantum field theory
3959:Quantum gauge theory
3785:
3705:
3663:along a closed loop
3559:
3504:
3423:
3263:
3183:
3142:
2975:The notion of quark
2776:
2711:
2689:FaddeevâPopov ghosts
2673:quantum field theory
2636:
2392:
2372:
2306:
2140:
2085:
2028:
1979:
1951:
1930:
1802:
1757:
1737:
1717:
1697:
1677:
1628:
1435:
1346:spontaneously broken
561:quantum field theory
109:Quantum field theory
87:Elementary particles
32:QCD (disambiguation)
6727:Atmospheric physics
6566:Classical mechanics
6494:branches of physics
6321:Split supersymmetry
6283:KaluzaâKlein theory
6156:Fermi's interaction
5992:Quantum information
5596:Quartic interaction
5394:proving confinement
5385:Particle data group
5370:2000PhT....53h..22W
5155:1978PhRvB..18.4789F
5113:1977JPhC...10L.537V
5078:1976PhLA...56..421M
5027:2007PrPNP..58..351B
4970:2010PhRvD..81c4504C
4934:Scientific American
4837:2000NuPhS..86..421E
4755:1971JMP....12.2259W
4718:1954PhRv...96..191Y
4660:1973PhLB...47..365F
4625:1965PhRv..139.1006H
4619:(4B): B1006âB1010.
4586:1964PhRvL..13..598G
4473:2010mgsp.book.....F
4442:1964PhL.....8..214G
4384:1956NCim....4S.848G
4345:1955PThPh..13..285N
4302:1953PThPh..10..581N
4191:. Nobel Web. 2004.
4165:1973PhRvL..30.1346P
4122:1973PhRvL..30.1343G
3967:FaddeevâPopov ghost
3855:
3808:
3054:(this includes the
2834:perturbation theory
2732:entropic elasticity
2632:to quarks, denoted
2417:structure constants
2327:
2284:
2265:
2224:
2192:
2160:
2121:, analogous to the
2105:
1940:{\displaystyle g\,}
1914:
1609:
1591:
1046:perturbation theory
701:perceived by humans
683:The three kinds of
559:. QCD is a type of
521:theoretical physics
6783:History of physics
6349:Superstring theory
6119:Strong interaction
5878:NambuâJona-Lasinio
5806:Higher dimensional
5713:WessâZuminoâWitten
5503:Noncommutative QFT
5412:Andreas S Kronfeld
5404:Andreas S Kronfeld
4910:
4879:quarkâgluon plasma
4791:2011-05-04 at the
4558:2007-05-23 at the
4392:10.1007/BF02748000
4354:10.1143/PTP.13.285
4311:10.1143/PTP.10.581
4033:Quarkâgluon plasma
3944:Quarkâgluon plasma
3914:Strong interaction
3870:
3838:
3794:
3737:
3699:asymptotic freedom
3695:entropy-elasticity
3653:
3523:
3497:However, here the
3484:
3409:
3241:
3165:
3104:quarkâgluon plasma
3068:Jet cross sections
3003:the history of QCD
2971:Experimental tests
2919:Effective theories
2860:
2796:
2720:
2653:
2603:Gluons are spin-1
2513:
2398:
2378:
2338:
2309:
2289:
2266:
2247:
2206:
2174:
2143:
2133:. It is given by:
2107:
2088:
2076:Gell-Mann matrices
2064:
2014:
1965:
1937:
1916:
1896:
1770:
1743:
1723:
1703:
1683:
1651:
1610:
1592:
1574:
1427:QCD Lagrangian is
1263:asymptotic freedom
1097:quarkâgluon plasma
1030:asymptotic freedom
1011:Heinrich Leutwyler
900:Albert Tavkhelidze
892:Nikolay Bogolyubov
888:Nikolay Bogolyubov
809:Kazuhiko Nishijima
716:strong interaction
617:Asymptotic freedom
591:. A large body of
533:strong interaction
84:
6811:
6810:
6798:Physics education
6747:Materials science
6714:Interdisciplinary
6672:Quantum mechanics
6459:
6458:
6382:
6381:
6257:Strong CP problem
6235:Hierarchy problem
6039:
6038:
5901:
5900:
5378:10.1063/1.1310117
5351:"QCD made simple"
5289:978-0-521-31535-7
5270:978-0-471-88741-6
5240:978-3-540-48535-3
5143:Physical Review B
4763:10.1063/1.1665530
4749:(10): 2259â2272.
4529:Preprint D-1968,
4257:"The Color Force"
4245:wikt:colour force
4231:978-0-8050-7253-2
4214:Gell-Mann, Murray
4159:(26): 1346â1349.
4116:(26): 1343â1346.
4088:978-3-642-14381-6
4050:YangâMills theory
4019:For experiments:
3963:BRST quantization
3934:Color confinement
3819:
3056:DrellâYan process
3039:Scaling violation
2650:
2572:weak interactions
2493:Kenneth G. Wilson
2401:{\displaystyle 8}
2381:{\displaystyle 1}
1746:{\displaystyle 3}
1726:{\displaystyle 1}
1706:{\displaystyle j}
1686:{\displaystyle i}
1572:
1473:
1365:chiral condensate
1201:YangâMills theory
1193:global symmetries
1083:announced by the
1028:The discovery of
1023:YangâMills theory
938:degree of freedom
797:Werner Heisenberg
603:Color confinement
575:. Gluons are the
517:
516:
165:Hierarchy problem
161:Strong CP problem
16:(Redirected from
6836:
6737:Chemical physics
6677:Particle physics
6603:Classical optics
6486:
6479:
6472:
6463:
6447:
6446:
6435:
6434:
6225:
6180:
6179:
6161:Weak hypercharge
6146:Weak interaction
6087:Particle physics
6066:
6059:
6052:
6043:
6031:
6030:
5948:Quantum dynamics
5621:YangâMillsâHiggs
5576:Non-linear sigma
5566:EulerâHeisenberg
5551:
5462:
5455:
5448:
5439:
5381:
5355:
5337:
5319:
5293:
5274:
5262:
5244:
5215:
5208:
5202:
5201:
5181:
5175:
5174:
5149:(9): 4789â4814.
5140:
5131:
5125:
5124:
5096:
5090:
5089:
5061:
5055:
5054:
5020:
4996:
4990:
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4963:
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4911:
4909:
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4872:
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4857:
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4795:
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4766:
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4643:
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4498:
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4495:
4483:
4477:
4476:
4460:
4454:
4453:
4423:
4417:
4410:
4404:
4403:
4371:Il Nuovo Cimento
4365:
4359:
4358:
4356:
4322:
4316:
4315:
4313:
4279:
4273:
4271:
4269:
4268:
4253:
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4236:
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4210:
4204:
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4201:
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4185:
4179:
4178:
4176:
4142:
4136:
4135:
4133:
4099:
4093:
4092:
4070:
3993:Perturbative QCD
3979:For techniques:
3900:
3895:
3894:
3879:
3877:
3876:
3871:
3865:
3864:
3854:
3849:
3837:
3836:
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3807:
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3292:
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3250:
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3235:
3225:
3224:
3214:
3213:
3201:
3200:
3174:
3172:
3171:
3166:
3154:
3153:
3132:gauge invariance
3018:three-jet events
3000:
2999:
2998:
2991:
2990:
2908:
2907:
2901:
2828:Perturbative QCD
2822:Perturbative QCD
2805:
2803:
2802:
2797:
2792:
2791:
2729:
2727:
2726:
2721:
2677:Feynman diagrams
2662:
2660:
2659:
2654:
2652:
2651:
2646:
2641:
2607:that also carry
2592:for each quark,
2591:
2590:
2586:
2569:
2568:
2564:
2559:
2558:
2554:
2524:
2523:
2519:
2469:metric signature
2455:whereas for the
2407:
2405:
2404:
2399:
2387:
2385:
2384:
2379:
2347:
2345:
2344:
2339:
2326:
2321:
2316:
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2298:
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2264:
2259:
2254:
2253:
2246:
2245:
2223:
2218:
2213:
2212:
2205:
2204:
2191:
2186:
2181:
2180:
2173:
2172:
2159:
2154:
2116:
2114:
2113:
2108:
2104:
2099:
2073:
2071:
2070:
2065:
2040:
2039:
2023:
2021:
2020:
2015:
2009:
2004:
2003:
1991:
1990:
1974:
1972:
1971:
1966:
1963:
1962:
1946:
1944:
1943:
1938:
1925:
1923:
1922:
1917:
1913:
1908:
1903:
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1894:
1886:
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1546:
1545:
1544:
1525:
1524:
1512:
1511:
1499:
1498:
1481:
1480:
1475:
1474:
1466:
1459:
1458:
1457:
1445:
1444:
1175:local symmetries
1168:particle physics
1115:
1108:Some definitions
1095:, including the
1089:non-perturbative
1058:perturbative QCD
1050:three-jet events
896:Boris Struminsky
882:
850:Boris Struminsky
825:. Gell-Mann and
805:Murray Gell-Mann
773:particle physics
744:
738:
737:
662:coined the word
660:Murray Gell-Mann
589:particle physics
509:
502:
495:
101:Particle physics
54:
45:particle physics
37:
21:
6844:
6843:
6839:
6838:
6837:
6835:
6834:
6833:
6814:
6813:
6812:
6807:
6771:
6757:Medical physics
6708:
6667:Nuclear physics
6636:
6630:Non-equilibrium
6552:
6524:
6496:
6490:
6460:
6455:
6423:
6378:
6336:Quantum gravity
6330:
6297:
6266:
6219:
6212:
6203:Higgs mechanism
6181:
6177:
6172:
6075:
6070:
6040:
6035:
6018:
5970:Quantum gravity
5897:
5856:Particle theory
5851:
5830:
5779:
5753:
5717:
5681:
5635:Low dimensional
5630:
5571:GinzburgâLandau
5542:
5533:Topological QFT
5471:
5466:
5353:
5348:
5345:
5296:
5290:
5277:
5271:
5249:Halzen, Francis
5247:
5241:
5226:
5223:
5221:Further reading
5218:
5209:
5205:
5198:10.1002/pi.1445
5183:
5182:
5178:
5138:
5133:
5132:
5128:
5098:
5097:
5093:
5063:
5062:
5058:
4998:
4997:
4993:
4945:
4944:
4940:
4928:
4924:
4900:
4883:
4882:
4877:gives way to a
4873:
4869:
4864:
4860:
4812:
4811:
4807:
4802:
4798:
4793:Wayback Machine
4781:
4768:
4740:
4739:
4735:
4705:Physical Review
4690:
4689:
4685:
4669:10.1.1.453.4712
4648:Physics Letters
4645:
4644:
4640:
4606:
4605:
4601:
4580:(20): 598â602.
4574:Phys. Rev. Lett
4571:
4570:
4566:
4560:Wayback Machine
4550:
4546:
4541:
4537:
4521:
4517:
4508:
4501:
4485:
4484:
4480:
4462:
4461:
4457:
4429:Physics Letters
4425:
4424:
4420:
4411:
4407:
4378:(S2): 848â866.
4367:
4366:
4362:
4324:
4323:
4319:
4281:
4280:
4276:
4266:
4264:
4255:
4254:
4250:
4243:
4239:
4232:
4212:
4211:
4207:
4198:
4196:
4187:
4186:
4182:
4144:
4143:
4139:
4101:
4100:
4096:
4089:
4072:
4071:
4067:
4063:
3905:For overviews:
3896:
3889:
3886:
3856:
3828:
3809:
3783:
3782:
3779:
3757:
3752:
3727:
3714:
3703:
3702:
3691:polymer physics
3672:
3637:
3621:
3596:
3580:
3562:
3557:
3556:
3550:
3507:
3502:
3501:
3494:are invariant.
3470:
3453:
3442:
3421:
3420:
3391:
3378:
3365:
3353:
3337:
3327:
3308:
3296:
3283:
3270:
3261:
3260:
3258:
3254:
3227:
3216:
3205:
3186:
3181:
3180:
3145:
3140:
3139:
3124:
3093:
3012:experiments at
2997:
2995:
2994:
2993:
2989:
2987:
2986:
2985:
2984:
2973:
2961:
2955:
2921:
2903:
2899:
2898:
2894:
2888:
2848:
2842:
2830:
2824:
2816:
2783:
2774:
2773:
2767:
2756:
2709:
2708:
2701:
2693:unitarity gauge
2669:
2634:
2633:
2596:and one of the
2588:
2584:
2583:
2566:
2562:
2561:
2556:
2552:
2551:
2521:
2517:
2516:
2505:
2454:
2444:
2413:
2390:
2389:
2370:
2369:
2304:
2303:
2231:
2196:
2164:
2138:
2137:
2083:
2082:
2031:
2026:
2025:
1995:
1982:
1977:
1976:
1954:
1949:
1948:
1928:
1927:
1873:
1869:
1868:
1846:
1836:
1810:
1806:
1805:
1800:
1799:
1760:
1755:
1754:
1735:
1734:
1715:
1714:
1695:
1694:
1675:
1674:
1631:
1626:
1625:
1622:
1551:
1533:
1513:
1503:
1490:
1486:
1482:
1463:
1438:
1433:
1432:
1425:gauge invariant
1417:
1374:
1370:
1361:
1355:
1343:
1339:
1334:
1328:
1323:
1317:
1308:
1293:
1291:Symmetry groups
1267:short distances
1259:
1216:flavor symmetry
1164:
1163:
1158:
1153:phase of matter
1119:QCD in the non-
1117:
1113:
1110:
1105:
1007:Harald Fritzsch
978:S-matrix theory
960:Richard Feynman
883:
876:
765:bubble chambers
761:
753:Main articles:
751:
727:electrodynamics
656:
513:
484:
483:
184:
176:
175:
171:
167:
163:
158:
150:
149:
145:
141:
137:
132:
124:
123:
121:Higgs mechanism
119:
115:
111:
107:
103:
98:
90:
81:
52:
35:
28:
23:
22:
15:
12:
11:
5:
6842:
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6832:
6831:
6826:
6816:
6815:
6809:
6808:
6806:
6805:
6800:
6795:
6790:
6785:
6779:
6777:
6773:
6772:
6770:
6769:
6764:
6759:
6754:
6749:
6744:
6739:
6734:
6729:
6724:
6718:
6716:
6710:
6709:
6707:
6706:
6701:
6700:
6699:
6694:
6689:
6679:
6674:
6669:
6664:
6663:
6662:
6657:
6646:
6644:
6638:
6637:
6635:
6634:
6633:
6632:
6627:
6620:Thermodynamics
6617:
6616:
6615:
6610:
6600:
6595:
6590:
6589:
6588:
6583:
6578:
6573:
6562:
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6553:
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6550:
6549:
6548:
6538:
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6504:
6502:
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6491:
6489:
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6481:
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6466:
6457:
6456:
6454:
6453:
6441:
6428:
6425:
6424:
6422:
6421:
6416:
6411:
6406:
6401:
6396:
6390:
6388:
6384:
6383:
6380:
6379:
6377:
6376:
6374:Twistor theory
6371:
6366:
6361:
6356:
6351:
6346:
6340:
6338:
6332:
6331:
6329:
6328:
6323:
6318:
6313:
6307:
6305:
6299:
6298:
6296:
6295:
6290:
6285:
6280:
6274:
6272:
6268:
6267:
6265:
6264:
6259:
6254:
6253:
6252:
6242:
6237:
6231:
6229:
6222:
6220:Standard Model
6214:
6213:
6211:
6210:
6205:
6200:
6195:
6189:
6187:
6183:
6182:
6175:
6173:
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6158:
6153:
6148:
6138:
6137:
6136:
6131:
6126:
6116:
6111:
6106:
6105:
6104:
6099:
6094:
6083:
6081:
6077:
6076:
6073:Standard Model
6071:
6069:
6068:
6061:
6054:
6046:
6037:
6036:
6023:
6020:
6019:
6017:
6016:
6011:
6006:
6005:
6004:
5994:
5989:
5984:
5979:
5978:
5977:
5967:
5966:
5965:
5955:
5950:
5945:
5940:
5935:
5930:
5925:
5920:
5915:
5913:Casimir effect
5909:
5907:
5903:
5902:
5899:
5898:
5896:
5895:
5890:
5888:Standard Model
5885:
5880:
5875:
5870:
5865:
5859:
5857:
5853:
5852:
5850:
5849:
5844:
5838:
5836:
5832:
5831:
5829:
5828:
5823:
5818:
5813:
5808:
5803:
5798:
5793:
5787:
5785:
5781:
5780:
5778:
5777:
5772:
5767:
5761:
5759:
5758:Superconformal
5755:
5754:
5752:
5751:
5746:
5741:
5739:SeibergâWitten
5736:
5731:
5725:
5723:
5722:Supersymmetric
5719:
5718:
5716:
5715:
5710:
5705:
5700:
5695:
5689:
5687:
5683:
5682:
5680:
5679:
5674:
5669:
5664:
5659:
5654:
5649:
5644:
5638:
5636:
5632:
5631:
5629:
5628:
5623:
5618:
5613:
5608:
5603:
5598:
5593:
5588:
5583:
5578:
5573:
5568:
5563:
5557:
5555:
5548:
5544:
5543:
5541:
5540:
5535:
5530:
5525:
5520:
5515:
5510:
5505:
5500:
5495:
5490:
5485:
5479:
5477:
5473:
5472:
5467:
5465:
5464:
5457:
5450:
5442:
5436:
5435:
5427:
5422:
5417:
5409:
5401:
5396:
5387:
5382:
5344:
5343:External links
5341:
5340:
5339:
5294:
5288:
5275:
5269:
5245:
5239:
5222:
5219:
5217:
5216:
5203:
5192:(7): 863â868.
5176:
5126:
5091:
5072:(5): 421â422.
5056:
5018:hep-ex/0606035
5011:(2): 351â386.
4991:
4938:
4922:
4907:
4903:
4899:
4896:
4893:
4890:
4867:
4858:
4828:hep-ph/9908318
4805:
4796:
4779:
4733:
4712:(1): 191â195.
4683:
4654:(4): 365â368.
4638:
4599:
4564:
4544:
4535:
4515:
4499:
4478:
4455:
4436:(3): 214â215.
4418:
4405:
4360:
4339:(3): 285â304.
4317:
4274:
4248:
4237:
4230:
4205:
4180:
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4064:
4062:
4059:
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3990:
3985:
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3975:
3969:
3956:
3948:
3947:
3946:
3941:
3936:
3931:
3926:
3921:
3916:
3911:
3909:Standard Model
3902:
3901:
3898:Physics portal
3885:
3882:
3869:
3863:
3859:
3853:
3848:
3845:
3841:
3835:
3831:
3825:
3818:
3815:
3806:
3801:
3797:
3793:
3790:
3777:
3755:
3750:
3734:
3730:
3726:
3721:
3717:
3713:
3710:
3670:
3650:
3647:
3644:
3640:
3634:
3631:
3628:
3624:
3620:
3617:
3614:
3609:
3606:
3603:
3599:
3593:
3590:
3587:
3583:
3578:
3574:
3569:
3565:
3548:
3520:
3517:
3514:
3510:
3483:
3477:
3473:
3466:
3463:
3460:
3456:
3449:
3445:
3441:
3438:
3435:
3430:
3408:
3404:
3398:
3394:
3390:
3385:
3381:
3377:
3372:
3368:
3360:
3356:
3350:
3347:
3344:
3340:
3334:
3330:
3326:
3321:
3318:
3315:
3311:
3303:
3299:
3295:
3290:
3286:
3282:
3277:
3273:
3268:
3256:
3252:
3240:
3234:
3230:
3223:
3219:
3212:
3208:
3204:
3199:
3196:
3193:
3189:
3163:
3160:
3157:
3152:
3148:
3123:
3120:
3091:
3084:
3083:
3080:
3071:
3065:
3062:Direct photons
3059:
3050:production at
3045:
3036:
2996:
2988:
2972:
2969:
2957:Main article:
2954:
2951:
2920:
2917:
2890:Main article:
2887:
2880:
2868:supercomputers
2844:Main article:
2841:
2838:
2826:Main article:
2823:
2820:
2815:
2812:
2795:
2790:
2786:
2782:
2765:
2754:
2719:
2716:
2700:
2697:
2668:
2665:
2649:
2645:
2504:
2501:
2474:The variables
2450:
2442:
2411:
2397:
2377:
2336:
2333:
2330:
2325:
2320:
2314:
2300:
2299:
2288:
2282:
2277:
2271:
2263:
2258:
2252:
2244:
2241:
2238:
2234:
2230:
2227:
2222:
2217:
2211:
2203:
2199:
2195:
2190:
2185:
2179:
2171:
2167:
2163:
2158:
2153:
2150:
2146:
2103:
2098:
2095:
2091:
2062:
2059:
2056:
2053:
2050:
2047:
2044:
2038:
2034:
2024:, wherein the
2012:
2008:
2002:
1998:
1994:
1989:
1985:
1961:
1957:
1935:
1912:
1907:
1901:
1893:
1890:
1885:
1880:
1876:
1872:
1867:
1864:
1861:
1856:
1853:
1849:
1843:
1839:
1835:
1830:
1827:
1822:
1817:
1813:
1809:
1786:Gamma matrices
1767:
1763:
1742:
1722:
1702:
1682:
1649:
1646:
1643:
1638:
1634:
1621:
1620:
1607:
1604:
1599:
1595:
1589:
1584:
1581:
1577:
1571:
1568:
1563:
1558:
1554:
1549:
1543:
1540:
1536:
1531:
1528:
1523:
1520:
1516:
1510:
1506:
1502:
1497:
1493:
1489:
1485:
1479:
1472:
1469:
1462:
1456:
1453:
1450:
1443:
1429:
1416:
1413:
1372:
1368:
1359:
1353:
1341:
1337:
1332:
1326:
1321:
1315:
1306:
1292:
1289:
1281:original model
1261:As mentioned,
1258:
1255:
1254:
1253:
1247:
1241:
1197:
1196:
1190:
1159:
1157:
1156:
1140:
1118:
1112:
1109:
1106:
1104:
1101:
1038:David Politzer
1015:Chen Ning Yang
874:
858:strange quarks
846:quantum number
831:Shoichi Sakata
769:spark chambers
750:
747:
669:Finnegans Wake
655:
652:
651:
650:
647:Yoichiro Nambu
636:
629:David Politzer
614:
585:Standard Model
577:force carriers
515:
514:
512:
511:
504:
497:
489:
486:
485:
482:
481:
476:
471:
466:
461:
456:
451:
446:
441:
436:
431:
426:
421:
416:
411:
406:
401:
396:
391:
386:
381:
376:
371:
366:
361:
356:
351:
346:
341:
336:
331:
326:
321:
316:
311:
306:
301:
296:
291:
286:
281:
276:
271:
266:
261:
256:
251:
246:
241:
236:
231:
226:
221:
216:
211:
206:
201:
196:
191:
185:
182:
181:
178:
177:
159:
156:
155:
152:
151:
133:
130:
129:
126:
125:
105:Standard Model
99:
96:
95:
92:
91:
85:
48:
47:
41:Standard Model
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6841:
6830:
6827:
6825:
6822:
6821:
6819:
6804:
6801:
6799:
6796:
6794:
6791:
6789:
6786:
6784:
6781:
6780:
6778:
6774:
6768:
6765:
6763:
6762:Ocean physics
6760:
6758:
6755:
6753:
6750:
6748:
6745:
6743:
6740:
6738:
6735:
6733:
6730:
6728:
6725:
6723:
6720:
6719:
6717:
6715:
6711:
6705:
6702:
6698:
6697:Modern optics
6695:
6693:
6690:
6688:
6685:
6684:
6683:
6680:
6678:
6675:
6673:
6670:
6668:
6665:
6661:
6658:
6656:
6653:
6652:
6651:
6648:
6647:
6645:
6643:
6639:
6631:
6628:
6626:
6623:
6622:
6621:
6618:
6614:
6611:
6609:
6606:
6605:
6604:
6601:
6599:
6596:
6594:
6591:
6587:
6584:
6582:
6579:
6577:
6574:
6572:
6569:
6568:
6567:
6564:
6563:
6561:
6559:
6555:
6547:
6546:Computational
6544:
6543:
6542:
6539:
6537:
6534:
6533:
6531:
6527:
6519:
6516:
6515:
6514:
6511:
6509:
6506:
6505:
6503:
6499:
6495:
6487:
6482:
6480:
6475:
6473:
6468:
6467:
6464:
6452:
6451:
6442:
6440:
6439:
6430:
6429:
6426:
6420:
6417:
6415:
6412:
6410:
6407:
6405:
6402:
6400:
6397:
6395:
6392:
6391:
6389:
6385:
6375:
6372:
6370:
6367:
6365:
6362:
6360:
6357:
6355:
6352:
6350:
6347:
6345:
6344:String theory
6342:
6341:
6339:
6337:
6333:
6327:
6324:
6322:
6319:
6317:
6314:
6312:
6309:
6308:
6306:
6304:
6303:Supersymmetry
6300:
6294:
6291:
6289:
6286:
6284:
6281:
6279:
6276:
6275:
6273:
6269:
6263:
6260:
6258:
6255:
6251:
6248:
6247:
6246:
6243:
6241:
6238:
6236:
6233:
6232:
6230:
6226:
6223:
6221:
6215:
6209:
6206:
6204:
6201:
6199:
6196:
6194:
6191:
6190:
6188:
6184:
6167:
6164:
6162:
6159:
6157:
6154:
6152:
6149:
6147:
6144:
6143:
6142:
6139:
6135:
6132:
6130:
6127:
6125:
6122:
6121:
6120:
6117:
6115:
6112:
6110:
6107:
6103:
6100:
6098:
6095:
6093:
6090:
6089:
6088:
6085:
6084:
6082:
6078:
6074:
6067:
6062:
6060:
6055:
6053:
6048:
6047:
6044:
6034:
6026:
6021:
6015:
6012:
6010:
6009:Quantum logic
6007:
6003:
6000:
5999:
5998:
5995:
5993:
5990:
5988:
5985:
5983:
5980:
5976:
5973:
5972:
5971:
5968:
5964:
5961:
5960:
5959:
5956:
5954:
5951:
5949:
5946:
5944:
5943:Quantum chaos
5941:
5939:
5936:
5934:
5931:
5929:
5926:
5924:
5921:
5919:
5918:Cosmic string
5916:
5914:
5911:
5910:
5908:
5904:
5894:
5891:
5889:
5886:
5884:
5881:
5879:
5876:
5874:
5871:
5869:
5866:
5864:
5861:
5860:
5858:
5854:
5848:
5845:
5843:
5840:
5839:
5837:
5833:
5827:
5824:
5822:
5819:
5817:
5814:
5812:
5809:
5807:
5804:
5802:
5799:
5797:
5794:
5792:
5791:Pure 4D N = 1
5789:
5788:
5786:
5782:
5776:
5773:
5771:
5768:
5766:
5763:
5762:
5760:
5756:
5750:
5747:
5745:
5742:
5740:
5737:
5735:
5732:
5730:
5727:
5726:
5724:
5720:
5714:
5711:
5709:
5706:
5704:
5701:
5699:
5696:
5694:
5691:
5690:
5688:
5684:
5678:
5675:
5673:
5672:ThirringâWess
5670:
5668:
5665:
5663:
5660:
5658:
5655:
5653:
5650:
5648:
5647:BulloughâDodd
5645:
5643:
5642:2D YangâMills
5640:
5639:
5637:
5633:
5627:
5624:
5622:
5619:
5617:
5614:
5612:
5609:
5607:
5604:
5602:
5599:
5597:
5594:
5592:
5589:
5587:
5584:
5582:
5579:
5577:
5574:
5572:
5569:
5567:
5564:
5562:
5559:
5558:
5556:
5552:
5549:
5545:
5539:
5536:
5534:
5531:
5529:
5526:
5524:
5521:
5519:
5518:String theory
5516:
5514:
5511:
5509:
5506:
5504:
5501:
5499:
5496:
5494:
5491:
5489:
5488:Axiomatic QFT
5486:
5484:
5483:Algebraic QFT
5481:
5480:
5478:
5474:
5470:
5463:
5458:
5456:
5451:
5449:
5444:
5443:
5440:
5434:
5431:
5428:
5426:
5423:
5421:
5418:
5416:
5413:
5410:
5408:
5405:
5402:
5400:
5397:
5395:
5391:
5388:
5386:
5383:
5379:
5375:
5371:
5367:
5363:
5359:
5358:Physics Today
5352:
5347:
5346:
5342:
5335:
5331:
5327:
5323:
5318:
5313:
5309:
5305:
5301:
5295:
5291:
5285:
5281:
5276:
5272:
5266:
5261:
5260:
5254:
5250:
5246:
5242:
5236:
5232:
5231:
5225:
5224:
5220:
5213:
5207:
5204:
5199:
5195:
5191:
5187:
5180:
5177:
5172:
5168:
5164:
5160:
5156:
5152:
5148:
5144:
5137:
5130:
5127:
5122:
5118:
5114:
5110:
5106:
5102:
5095:
5092:
5087:
5083:
5079:
5075:
5071:
5067:
5066:Phys. Lett. A
5060:
5057:
5052:
5048:
5044:
5040:
5036:
5032:
5028:
5024:
5019:
5014:
5010:
5006:
5002:
4995:
4992:
4987:
4983:
4979:
4975:
4971:
4967:
4962:
4957:
4954:(3): 034504.
4953:
4949:
4942:
4939:
4935:
4931:
4926:
4923:
4905:
4901:
4897:
4894:
4891:
4888:
4880:
4876:
4871:
4868:
4862:
4859:
4854:
4850:
4846:
4842:
4838:
4834:
4829:
4824:
4820:
4816:
4809:
4806:
4800:
4797:
4794:
4790:
4787:
4782:
4776:
4772:
4767:Reprinted in
4764:
4760:
4756:
4752:
4748:
4744:
4743:J. Math. Phys
4737:
4734:
4728:
4723:
4719:
4715:
4711:
4707:
4706:
4701:
4697:
4693:
4687:
4684:
4679:
4675:
4670:
4665:
4661:
4657:
4653:
4649:
4642:
4639:
4634:
4630:
4626:
4622:
4618:
4614:
4610:
4603:
4600:
4595:
4591:
4587:
4583:
4579:
4575:
4568:
4565:
4561:
4557:
4554:
4548:
4545:
4539:
4536:
4532:
4528:
4524:
4519:
4516:
4512:
4506:
4504:
4500:
4494:
4489:
4482:
4479:
4474:
4470:
4466:
4459:
4456:
4451:
4447:
4443:
4439:
4435:
4431:
4430:
4422:
4419:
4415:
4409:
4406:
4401:
4397:
4393:
4389:
4385:
4381:
4377:
4373:
4372:
4364:
4361:
4355:
4350:
4346:
4342:
4338:
4334:
4333:
4328:
4321:
4318:
4312:
4307:
4303:
4299:
4295:
4291:
4290:
4285:
4278:
4275:
4262:
4258:
4252:
4249:
4246:
4241:
4238:
4233:
4227:
4223:
4219:
4215:
4209:
4206:
4194:
4190:
4184:
4181:
4175:
4170:
4166:
4162:
4158:
4154:
4153:
4148:
4141:
4138:
4132:
4127:
4123:
4119:
4115:
4111:
4110:
4105:
4098:
4095:
4090:
4084:
4080:
4076:
4069:
4066:
4060:
4056:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4034:
4031:
4029:
4026:
4024:
4021:
4020:
4018:
4014:
4011:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3989:
3988:1/N expansion
3986:
3984:
3981:
3980:
3978:
3973:
3970:
3968:
3964:
3960:
3957:
3955:
3952:
3951:
3950:For details:
3949:
3945:
3942:
3940:
3937:
3935:
3932:
3930:
3927:
3925:
3922:
3920:
3917:
3915:
3912:
3910:
3907:
3906:
3904:
3903:
3899:
3893:
3888:
3883:
3881:
3867:
3861:
3857:
3851:
3846:
3843:
3839:
3833:
3829:
3823:
3813:
3804:
3799:
3795:
3791:
3788:
3780:
3773:
3769:
3765:
3759:
3753:
3732:
3728:
3724:
3719:
3715:
3708:
3700:
3696:
3692:
3687:
3685:
3679:
3675:
3673:
3666:
3648:
3645:
3642:
3638:
3632:
3629:
3626:
3622:
3618:
3615:
3612:
3607:
3604:
3601:
3597:
3591:
3588:
3585:
3581:
3576:
3572:
3567:
3563:
3554:
3547:
3544:For positive
3542:
3540:
3536:
3518:
3515:
3512:
3508:
3500:
3495:
3481:
3475:
3471:
3464:
3461:
3458:
3454:
3447:
3443:
3439:
3436:
3433:
3406:
3396:
3392:
3388:
3383:
3379:
3370:
3366:
3358:
3354:
3348:
3345:
3342:
3338:
3332:
3328:
3319:
3316:
3313:
3309:
3301:
3297:
3293:
3288:
3284:
3275:
3271:
3238:
3232:
3228:
3221:
3217:
3210:
3206:
3202:
3197:
3194:
3191:
3187:
3178:
3161:
3158:
3155:
3150:
3146:
3137:
3133:
3129:
3121:
3119:
3116:
3112:
3107:
3105:
3101:
3097:
3089:
3081:
3079:
3075:
3072:
3069:
3066:
3063:
3060:
3057:
3053:
3049:
3046:
3044:
3040:
3037:
3034:
3030:
3029:
3028:
3025:
3023:
3019:
3015:
3011:
3006:
3004:
2982:
2978:
2970:
2968:
2966:
2960:
2959:QCD sum rules
2953:QCD sum rules
2952:
2950:
2948:
2944:
2940:
2936:
2931:
2927:
2918:
2916:
2914:
2910:
2906:
2893:
2892:1/N expansion
2885:
2881:
2879:
2877:
2873:
2869:
2865:
2857:
2852:
2847:
2839:
2837:
2835:
2829:
2821:
2819:
2813:
2811:
2809:
2788:
2784:
2771:
2764:
2760:
2753:
2749:
2745:
2741:
2737:
2733:
2717:
2714:
2706:
2698:
2696:
2694:
2690:
2686:
2682:
2678:
2674:
2666:
2664:
2631:
2626:
2624:
2621:
2617:
2614:
2610:
2609:color charges
2606:
2601:
2599:
2595:
2581:
2580:baryon number
2577:
2573:
2549:
2546:
2542:
2539:
2535:
2531:
2528:that carry a
2527:
2509:
2502:
2500:
2498:
2494:
2491:(named after
2490:
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2477:
2472:
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2458:
2453:
2449:
2445:
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2375:
2368:running from
2367:
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2120:
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2057:
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2010:
2006:
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1996:
1992:
1987:
1983:
1959:
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1791:
1790:Lorentz group
1787:
1783:
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1720:
1713:running from
1700:
1680:
1673:, indexed by
1672:
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1324:
1313:
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1302:
1301:abelian group
1299:: this is an
1298:
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1173:
1172:
1171:
1169:
1162:
1154:
1150:
1146:
1145:
1141:
1138:
1137:atomic nuclei
1134:
1133:energy scales
1130:
1129:
1125:
1124:
1122:
1107:
1102:
1100:
1098:
1094:
1090:
1086:
1082:
1078:
1074:
1069:
1067:
1063:
1059:
1055:
1051:
1047:
1043:
1042:Frank Wilczek
1039:
1035:
1031:
1026:
1024:
1020:
1016:
1012:
1008:
1004:
999:
997:
993:
989:
985:
984:James Bjorken
981:
979:
975:
969:
967:
966:
961:
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947:
943:
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869:
867:
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859:
855:
851:
847:
842:
840:
836:
832:
828:
824:
823:Yuval Ne'eman
820:
819:
818:eightfold way
814:
810:
806:
802:
798:
794:
793:Eugene Wigner
790:
786:
782:
778:
774:
770:
766:
760:
756:
748:
746:
743:
732:
728:
723:
721:
720:nuclear force
717:
713:
709:
704:
702:
698:
694:
690:
686:
681:
679:
675:
671:
670:
665:
661:
653:
648:
644:
640:
637:
634:
630:
626:
625:Frank Wilczek
622:
618:
615:
612:
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604:
601:
600:
599:
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582:
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510:
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49:
46:
42:
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6722:Astrophysics
6536:Experimental
6448:
6436:
6326:Supergravity
6186:Constituents
6166:Weak isospin
6128:
6124:Color charge
6114:Gauge theory
6024:
5953:Quantum foam
5893:Stueckelberg
5847:ChernâSimons
5784:Supergravity
5590:
5523:Supergravity
5508:Gauge theory
5414:
5406:
5364:(8): 22â28.
5361:
5357:
5307:
5303:
5279:
5258:
5253:Martin, Alan
5229:
5206:
5189:
5185:
5179:
5146:
5142:
5129:
5104:
5100:
5094:
5069:
5065:
5059:
5008:
5004:
4994:
4951:
4948:Phys. Rev. D
4947:
4941:
4933:
4925:
4874:
4870:
4861:
4818:
4814:
4808:
4799:
4770:
4746:
4742:
4736:
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4703:
4686:
4651:
4647:
4641:
4616:
4612:
4602:
4577:
4573:
4567:
4547:
4538:
4523:N. Bogolubov
4518:
4481:
4464:
4458:
4433:
4427:
4421:
4408:
4375:
4369:
4363:
4336:
4330:
4320:
4293:
4287:
4277:
4265:. Retrieved
4251:
4240:
4217:
4208:
4197:. Retrieved
4183:
4156:
4150:
4140:
4113:
4107:
4097:
4074:
4068:
4008:Chiral model
3954:Gauge theory
3775:
3771:
3760:
3748:
3688:
3680:
3676:
3668:
3664:
3545:
3543:
3534:
3498:
3496:
3176:
3136:spin glasses
3125:
3108:
3100:quark matter
3096:form factors
3085:
3070:in colliders
3048:Vector boson
3026:
3007:
2974:
2963:Based on an
2962:
2947:chiral model
2922:
2904:
2895:
2883:
2861:
2855:
2831:
2817:
2807:
2769:
2762:
2751:
2739:
2702:
2670:
2627:
2622:
2615:
2602:
2576:weak isospin
2540:
2534:Dirac fields
2530:color charge
2514:
2486:
2484:
2479:
2475:
2473:
2465:relativistic
2464:
2460:
2456:
2451:
2447:
2440:
2436:
2432:
2431:indices are
2428:
2424:
2420:
2409:
2365:
2361:
2357:
2350:gluon fields
2301:
2126:
2080:
1795:Herein, the
1794:
1784:; the Îł are
1623:
1418:
1405:
1393:
1389:flavor SU(3)
1388:
1385:
1357:
1340:(1) × U
1330:
1319:
1304:
1294:
1284:
1280:
1276:
1270:
1266:
1262:
1260:
1249:
1243:
1237:
1220:
1215:
1213:
1209:color charge
1198:
1187:gauge bosons
1183:gauge theory
1165:
1144:Quark matter
1142:
1126:
1121:perturbative
1093:quark matter
1070:
1027:
1019:Robert Mills
1000:
982:
970:
963:
958:
952:
950:
942:gauge bosons
909:
885:
871:
843:
827:George Zweig
816:
762:
724:
711:
708:colour force
707:
705:
693:color charge
682:
677:
667:
663:
657:
597:
572:
547:such as the
539:mediated by
528:
524:
518:
138:
131:Constituents
113:Gauge theory
6625:Statistical
6541:Theoretical
6518:Engineering
6387:Experiments
6278:Technicolor
6240:Dark matter
6134:Quark model
6102:Higgs boson
6097:Gauge boson
5835:Topological
5749:WessâZumino
5662:Sine-Gordon
5652:GrossâNeveu
5561:BornâInfeld
5528:Thermal QFT
5107:(18): 537.
4875:Confinement
4692:Yang, C. N.
3983:Lattice QCD
3553:frustration
2981:quark model
2864:lattice QCD
2846:Lattice QCD
2840:Lattice QCD
2740:confinement
2594:hypercharge
2582:, which is
2574:as part of
2545:gauge group
2488:Wilson loop
2471:(+ â â â).
2081:The symbol
1325:) × SU
1128:Confinement
1077:lattice QCD
1073:confinement
1034:David Gross
801:strangeness
781:fundamental
712:color force
674:James Joyce
654:Terminology
621:David Gross
611:lattice QCD
309:Chamberlain
157:Limitations
6818:Categories
6742:Geophysics
6732:Biophysics
6576:Analytical
6529:Approaches
6394:Gran Sasso
6218:Beyond the
6193:CKM matrix
6080:Background
5616:YangâMills
5317:2212.11107
5212:Emil Artin
4785:Abstract:
4780:9971950707
4296:(5): 581.
4267:2007-08-29
4199:2010-10-24
4061:References
3939:QCD matter
3251:Here the Δ
2915:approach.
2759:Bag models
1421:Lagrangian
1415:Lagrangian
1396:QCD vacuum
1381:instantons
1350:QCD vacuum
1336:) × U
1285:dual model
1231:projection
658:Physicist
279:Iliopoulos
189:Rutherford
183:Scientists
143:CKM matrix
97:Background
6692:Molecular
6593:Acoustics
6586:Continuum
6581:Celestial
6571:Newtonian
6558:Classical
6501:Divisions
6025:See also:
5744:Super QCD
5698:Liouville
5686:Conformal
5657:Schwinger
5334:1434-6052
5043:0146-6410
4986:119216789
4961:0912.3181
4898:⋅
4892:≈
4696:Mills, R.
4664:CiteSeerX
4613:Phys. Rev
4493:0904.0343
4400:121017243
4222:Owl Books
3858:ψ
3834:μ
3830:γ
3817:¯
3814:ψ
3800:μ
3789:∝
3725:≪
3716:λ
3712:←
3440:∑
3437:−
3393:ϵ
3389:⋅
3376:→
3355:ϵ
3329:ϵ
3325:→
3298:ϵ
3294:⋅
3281:→
3229:ϵ
3207:ϵ
3159:±
3115:glueballs
3052:colliders
2909:expansion
2886:expansion
2870:like the
2794:⟩
2781:⟨
2715:∝
2648:¯
2319:μ
2276:ν
2257:μ
2216:μ
2202:ν
2198:∂
2194:−
2184:ν
2170:μ
2166:∂
2152:ν
2149:μ
2097:ν
2094:μ
2055:…
2033:λ
1997:λ
1906:μ
1860:−
1848:δ
1842:μ
1838:∂
1816:μ
1766:μ
1633:ψ
1606:ν
1603:μ
1583:ν
1580:μ
1562:−
1553:ψ
1535:δ
1527:−
1509:μ
1496:μ
1492:γ
1471:¯
1468:ψ
1223:chirality
1203:) of the
1179:spacetime
992:electrons
920:Greenberg
916:up quarks
563:called a
469:de Mayolo
414:Schwinger
354:Kobayashi
244:Gell-Mann
209:Sudarshan
6438:Category
6419:Tevatron
6271:Theories
6228:Evidence
6092:Fermions
5821:Type IIB
5816:Type IIA
5801:4D N = 8
5796:4D N = 1
5765:6D (2,0)
5729:4D N = 1
5708:Polyakov
5667:Thirring
5476:Theories
5255:(1984).
5051:14915298
4853:18237543
4789:Archived
4698:(1954).
4556:Archived
4261:Archived
4216:(1995).
4193:Archived
4079:Springer
3884:See also
3102:and the
2945:and the
2854:⟨
2748:nucleons
2667:Dynamics
2526:fermions
2497:confined
2415:are the
2348:are the
2074:are the
1123:regime:
912:Î baryon
875:â
862:fermions
535:between
459:Guralnik
404:Politzer
379:'t Hooft
334:Weinberg
329:Majorana
319:Schwartz
284:Lederman
269:Anderson
259:Friedman
219:Anderson
214:Davis Jr
199:Chadwick
6776:Related
6660:General
6655:Special
6513:Applied
6450:Commons
6414:Super-K
6250:problem
5923:History
5906:Related
5703:Minimal
5554:Regular
5366:Bibcode
5171:1446867
5151:Bibcode
5109:Bibcode
5074:Bibcode
5023:Bibcode
4966:Bibcode
4833:Bibcode
4751:Bibcode
4714:Bibcode
4656:Bibcode
4621:Bibcode
4582:Bibcode
4469:Bibcode
4438:Bibcode
4380:Bibcode
4341:Bibcode
4298:Bibcode
4161:Bibcode
4118:Bibcode
3747:(where
3684:duality
3539:entropy
3113:called
3088:lattice
3076:at the
2977:flavors
2913:AdS/CFT
2902:⁄
2814:Methods
2772:; i.e.
2685:photons
2587:⁄
2565:⁄
2555:⁄
2543:of the
2536:in the
2520:⁄
2433:trivial
1780:is the
1665:of the
1423:. The
1401:isospin
1394:In the
1377:anomaly
1348:by the
965:partons
953:defined
905:Trieste
854:hyperon
835:flavors
789:isospin
777:hadrons
749:History
729:", the
553:neutron
545:hadrons
444:Englert
419:Wilczek
384:Veltman
359:Maskawa
314:Cabibbo
274:Glashow
249:Kendall
234:Feynman
194:Thomson
6687:Atomic
6642:Modern
6492:Major
5863:Chiral
5811:Type I
5626:Yukawa
5547:Models
5332:
5310:(12).
5286:
5267:
5237:
5169:
5049:
5041:
4984:
4851:
4777:
4666:
4414:online
4398:
4228:
4085:
3929:Hadron
3535:gluons
3111:gluons
2992:Δ
2744:mesons
2736:rubber
2605:bosons
2503:Fields
2408:; and
2302:where
1669:gauge
1624:where
1312:chiral
1244:Vector
1238:Chiral
1103:Theory
1064:, at
946:gluons
944:: the
839:quarks
785:charge
742:chrĆma
685:charge
641:, the
549:proton
541:gluons
537:quarks
474:Lattes
464:Kibble
424:Cronin
409:Reines
374:Yukawa
289:Maiani
264:Powell
254:Taylor
239:Rubbia
6316:NMSSM
6002:links
5975:links
5963:links
5883:NMSSM
5868:Fermi
5611:Soler
5581:Proca
5354:(PDF)
5312:arXiv
5139:(PDF)
5047:S2CID
5013:arXiv
4982:S2CID
4956:arXiv
4849:S2CID
4823:arXiv
4533:1965.
4531:Dubna
4488:arXiv
4396:S2CID
3924:Gluon
3919:Quark
3255:and Δ
3022:PETRA
2872:QCDOC
2734:of a
2705:meson
2548:SU(3)
2427:, or
2129:, in
1671:group
1667:SU(3)
1277:large
1250:Axial
1205:SU(3)
1054:PETRA
1021:(see
1003:color
935:gauge
932:SU(3)
928:Nambu
811:(see
736:ÏÏáż¶ÎŒÎ±
733:word
731:Greek
714:) or
697:color
664:quark
573:color
569:SU(3)
479:Zweig
454:Hagen
449:Brout
439:Higgs
434:Vleck
429:Fitch
399:Pauli
389:Gross
364:Mills
349:Salam
304:Nambu
299:Cowan
229:Dirac
224:Fermi
6613:Wave
6508:Pure
6311:MSSM
5873:MSSM
5770:ABJM
5677:Toda
5392:for
5330:ISSN
5284:ISBN
5265:ISBN
5235:ISBN
5167:OSTI
5039:ISSN
4775:ISBN
4527:JINR
4511:JINR
4226:ISBN
4083:ISBN
3965:and
3175:for
3031:The
3014:SLAC
2808:area
2746:and
2560:or +
2478:and
2364:and
1693:and
1272:dual
1227:spin
1066:CERN
1040:and
1017:and
1009:and
996:SLAC
922:and
898:and
879:JINR
807:and
795:and
787:and
767:and
757:and
710:(or
623:and
557:pion
555:and
394:Pais
369:Yang
344:Ward
324:Perl
294:Meer
204:Bose
6608:Ray
6409:SNO
6404:LHC
6399:INO
5826:11D
5374:doi
5322:doi
5194:doi
5159:doi
5117:doi
5082:doi
5031:doi
4974:doi
4841:doi
4759:doi
4722:doi
4674:doi
4652:47B
4629:doi
4617:139
4590:doi
4446:doi
4388:doi
4349:doi
4306:doi
4169:doi
4126:doi
3078:LEP
3020:at
2928:is
2695:).
2681:QED
2459:or
2443:abc
2412:abc
2388:to
1733:to
1297:QED
1062:LEP
1052:at
990:of
924:Han
868:):
803:by
791:by
672:by
587:of
529:QCD
519:In
339:Lee
43:of
6820::
5842:BF
5372:.
5362:53
5360:.
5356:.
5328:.
5320:.
5308:83
5306:.
5302:.
5251:;
5190:53
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5165:.
5157:.
5147:18
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5141:.
5115:.
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5070:56
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5045:.
5037:.
5029:.
5021:.
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5003:.
4980:.
4972:.
4964:.
4952:81
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4906:12
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4839:.
4831:.
4819:86
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4757:.
4747:12
4745:.
4720:.
4710:96
4708:.
4702:.
4694:;
4672:.
4662:.
4650:.
4627:.
4615:.
4611:.
4588:.
4578:13
4576:.
4502:^
4444:.
4432:.
4416:).
4394:.
4386:.
4374:.
4347:.
4337:13
4335:.
4329:.
4304:.
4294:10
4292:.
4286:.
4259:.
4224:.
4220:.
4167:.
4157:30
4155:.
4149:.
4124:.
4114:30
4112:.
4106:.
4081:.
4077:.
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