6470:
5607:
6465:{\displaystyle {\begin{aligned}Z&=\exp \left(-i\ g\int \mathrm {d} ^{4}x\ {\frac {\delta }{i\ \delta \ {\bar {\varepsilon }}^{a}(x)}}\ f^{abc}\partial _{\mu }\ {\frac {i\ \delta }{\delta \ j_{\mu }^{b}(x)}}\ {\frac {i\ \delta }{\delta \ \varepsilon ^{c}(x)}}\right)\\&\qquad \times \exp \left(-i\ g\int \mathrm {d} ^{4}x\ f^{abc}\partial _{\mu }{\frac {i\ \delta }{\delta \ j_{\nu }^{a}(x)}}{\frac {i\ \delta }{\delta \ j_{\mu }^{b}(x)}}\ {\frac {i\ \delta }{\delta \ j^{c\nu }(x)}}\right)\\&\qquad \qquad \times \exp \left(-i\ {\frac {g^{2}}{4}}\int \mathrm {d} ^{4}x\ f^{abc}\ f^{ars}{\frac {i\ \delta }{\delta \ j_{\mu }^{b}(x)}}\ {\frac {i\ \delta }{\delta \ j_{\nu }^{c}(x)}}\ {\frac {\ i\delta }{\delta \ j^{r\mu }(x)}}{\frac {i\ \delta }{\delta \ j^{s\nu }(x)}}\right)\\&\qquad \qquad \qquad \times Z_{0}\end{aligned}}}
1693:
1702:
60:
1414:... I was at Brookhaven also ... and was assigned to the same office as Yang. Yang, who has demonstrated on a number of occasions his generosity to physicists beginning their careers, told me about his idea of generalizing gauge invariance and we discussed it at some length ... I was able to contribute something to the discussions, especially with regard to the quantization procedures, and to a small degree in working out the formalism; however, the key ideas were Yang's."
7053:). In this case, large computational resources are needed to be sure the correct limit of infinite volume (smaller lattice spacing) is obtained. This is the limit the results must be compared with. Smaller spacing and larger coupling are not independent of each other, and larger computational resources are needed for each. As of today, the situation appears somewhat satisfactory for the hadronic spectrum and the computation of the gluon and ghost propagators, but the
8488:
1713:
7045:. In the opposite limit, the infrared limit, the situation is the opposite, as the coupling is too large for perturbation theory to be reliable. Most of the difficulties that research meets is just managing the theory at low energies. That is the interesting case, being inherent to the description of hadronic matter and, more generally, to all the observed bound states of gluons and quarks and their confinement (see
6833:
1722:
5134:
6481:
5595:
5574:
4598:
1432:
to provide an explanation for isospin conservation in collisions involving the strong interactions. Yang's presentation of the work at
Princeton in February 1954 was challenged by Pauli, asking about the mass in the field developed with the gauge invariance idea. Pauli knew that this might be an
3447:
1656:
or the quantization of it. Because Pauli found that his theory "leads to some rather unphysical shadow particles", he refrained from publishing his results formally. Although Pauli did not publish his six-dimensional theory, he gave two seminar lectures about it in Zürich in
November 1953.
1992:
7811:
6828:{\displaystyle Z_{0}=\exp \left(-\int \mathrm {d} ^{4}x\ \mathrm {d} ^{4}y\ {\bar {\varepsilon }}^{a}(x)\ C^{ab}(x-y)\ \varepsilon ^{b}(y)\right)\exp \left({\tfrac {1}{2}}\int \mathrm {d} ^{4}x\ \mathrm {d} ^{4}y\ j_{\mu }^{a}(x)\ D^{ab\mu \nu }(x-y)\ j_{\nu }^{b}(y)\right)\ }
2732:
2221:
5254:
7104:
consists, especially, in a proof of the conjecture that the lowest excitations of a pure Yang–Mills theory (i.e. without matter fields) have a finite mass-gap with regard to the vacuum state. Another open problem, connected with this conjecture, is a proof of the
1672:
chose not to publish their work. Shortly after Yang and Mills published their paper in
October 1954, Salam encouraged Shaw to publish his work to mark his contribution. Shaw declined, and instead it only forms a chapter of his PhD thesis published in 1956.
3862:
1433:
issue as he had worked on applying gauge invariance but chose not to publish it, viewing the massless excitations of the theory to be "unphysical 'shadow particles'". Yang and Mills published in
October 1954; near the end of the paper, they admit:
5368:
4110:
7011:
are zero and so there is no coupling. In the non-abelian case, the ghost field appears as a useful way to rewrite the quantum field theory without physical consequences on the observables of the theory such as cross sections or decay rates.
7341:
5129:{\displaystyle {\begin{aligned}Z&=\int \ \exp {\Bigl \{}i\ S_{F}\ \left+i\ S_{gf}\left+i\ S_{g}\left{\Bigr \}}\\&\exp \left\{i\int \mathrm {d} ^{4}x\ j_{\mu }^{a}(x)A^{a\mu }(x)+i\int \mathrm {d} ^{4}x\ \left\right\}\end{aligned}}}
3125:
5357:
2854:
The field has the property of being self-interacting and the equations of motion that one obtains are said to be semilinear, as nonlinearities are both with and without derivatives. This means that one can manage this theory only by
6970:
3288:
2431:
1397:
Yang's core idea was to look for a conserved quantity in nuclear physics comparable to electric charge and use it to develop a corresponding gauge theory comparable to electrodynamics. He settled on conservation of
1863:
3659:
2579:
3273:
2849:
3763:
3198:
2998:
3929:
2290:
2052:
5612:
4603:
7030:. The relevance of this result is due to the fact that a Yang–Mills theory that describes strong interaction and asymptotic freedom permits proper treatment of experimental results coming from
1402:, a quantum number that distinguishes a neutron from a proton, but he made no progress on a theory. Taking a break from Princeton in the summer of 1953, Yang met a collaborator who could help:
5145:
1612:
has not been theoretically proven, though it is a consistent experimental observation. This shows why QCD confinement at low energy is a mathematical problem of great relevance, and why the
7112:
In physics the survey of Yang–Mills theories does not usually start from perturbation analysis or analytical methods, but more recently from systematic application of numerical methods to
7081:. Renormalizability is obtained even if the gauge bosons described by this theory are massive, as in the electroweak theory, provided the mass is only an "acquired" one, generated by the
2569:
4559:
3772:
5569:{\displaystyle \ S_{g}=-\int \mathrm {d} ^{4}x\ \left({\bar {c}}^{a}\ \partial _{\mu }\partial ^{\mu }c^{a}+g\ {\bar {c}}^{a}\ f^{abc}\ \partial _{\mu }\ A^{b\mu }\ c^{c}\right)\ }
7037:
To obtain the behavior of the Yang–Mills theory at high energies, and so to prove asymptotic freedom, one applies perturbation theory assuming a small coupling. This is verified
2922:
6869:
For quantum electrodynamics the ghost field decouples because the gauge group is abelian. This can be seen from the coupling between the gauge field and the ghost field that is
3978:
3970:
2479:
2326:
4281:
4200:
1608:
at lower energies in quantum chromodynamics is not completely understood due to the difficulties of managing such a theory with a strong coupling. This may be the reason why
7088:
The mathematics of the Yang–Mills theory is a very active field of research, yielding e.g. invariants of differentiable structures on four-dimensional manifolds via work of
1350:
7009:
4568:. This problem was already known for quantum electrodynamics but here becomes more severe due to non-abelian properties of the gauge group. A way out has been given by
2028:
7918:
1275:
proved that every conserved physical quantity has a matching symmetry, and culminated in 1928 when he published his book applying the geometrical theory of symmetry (
3008:
1383:
1320:
1176:
8341:
8151:
5265:
1455:
8233:
8192:
7171:
4297:
the coupling is dimensionless and both the field and the square of the coupling have the same dimensions of the field and the coupling of a massless quartic
7851:
7136:
229:
39:
Yang–Mills theory and the mass gap. Quantum particles described by the theory have mass but the classical waves of the field travel at the speed of light.
3442:{\displaystyle \ \left(D_{\mu }\ F_{\nu \kappa }\right)^{a}+\left(D_{\kappa }\ F_{\mu \nu }\right)^{a}+\left(D_{\nu }\ F_{\kappa \mu }\right)^{a}=0\ }
269:
7971:
6872:
2338:
7065:
resonance is not seen in any of such lattice computations and contrasting interpretations have been put forward. This is a hotly debated issue.
7996:
8100:
7214:
7199:
7101:
1613:
8331:
7726:
7324:
8223:
7911:
1987:{\displaystyle \ {\mathcal {L}}_{\mathrm {gf} }=-{\tfrac {1}{2}}\operatorname {tr} (F^{2})=-{\tfrac {1}{4}}F^{a\mu \nu }F_{\mu \nu }^{a}\ }
42:
1293:
in 1922, three years before working on his equation, connected Weyl's group concept to electron charge. Schrödinger showed that the group
1034:
8079:
7219:
7961:
7151:
7503:
1169:
2727:{\displaystyle \ F_{\mu \nu }^{a}=\partial _{\mu }A_{\nu }^{a}-\partial _{\nu }A_{\mu }^{a}+g\ f^{abc}\ A_{\mu }^{b}\ A_{\nu }^{c}\ }
8491:
8171:
7775:
7749:
7354:
799:
3461:
8421:
8228:
7991:
3206:
1664:
also developed a non-Abelian gauge theory for nuclear forces. However, the theory needed massless particles in order to maintain
1605:
8024:
2862:
Note that the transition between "upper" ("contravariant") and "lower" ("covariant") vector or tensor components is trivial for
8381:
8284:
8264:
7904:
72:
2746:
8187:
7946:
7941:
7189:
3667:
3133:
2927:
2216:{\displaystyle \ \operatorname {tr} \left(T^{a}\ T^{b}\right)={\tfrac {1}{2}}\delta ^{ab}\ ,\qquad \left=i\ f^{abc}\ T^{c}~.}
1824:
1411:
1385:
group transformations played a central role. Many physicists thought there must be an analog for the dynamics of nucleons.
347:
3870:
2237:
7843:
5249:{\displaystyle S_{F}=-{\tfrac {1}{2}}\int \mathrm {d} ^{4}x\ \operatorname {tr} \left(F^{\mu \nu }\ F_{\mu \nu }\right)\ }
1633:
1503:
1162:
186:
146:
8336:
8460:
7986:
904:
829:
176:
7582:
Yndurain, F.J.; Garcia-Martin, R.; Pelaez, J.R. (2007). "Experimental status of the ππ isoscalar S wave at low energy:
4589:
342:
8455:
8249:
7838:
1591:
279:
8029:
4585:
1598:. In the current epoch the strong interaction is not unified with the electroweak interaction, but from the observed
1480:. This prompted a significant restart of Yang–Mills theory studies that proved successful in the formulation of both
7874:
7878:
7146:
7141:
7093:
1692:
1267:
All known fundamental interactions can be described in terms of gauge theories, but working this out took decades.
1014:
181:
8197:
1701:
332:
7859:
7097:
7031:
4314:
1855:
1649:
1617:
274:
7209:
7126:
1841:
1682:
8433:
7374:
7077:, in 1972, worked out their renormalization, relying on a formulation of the problem worked out by his advisor
7061:
spectra are yet a questioned matter in view of the experimental observation of such exotic states. Indeed, the
5591:
fixes the gauge's choice for the quantization. Feynman's rules obtained from this functional are the following
3857:{\displaystyle \ {\tilde {F}}^{\mu \nu }={\tfrac {1}{2}}\varepsilon ^{\mu \nu \rho \sigma }F_{\rho \sigma }\ ,}
2508:
1403:
1197:
834:
459:
352:
289:
249:
8305:
8130:
8105:
7156:
5601:
These rules for
Feynman's diagrams can be obtained when the generating functional given above is rewritten as
4581:
4327:
1641:
824:
8510:
8161:
8044:
7741:
7521:
7480:
6859:
4564:
but this integral has no meaning as it is because the potential vector can be arbitrarily chosen due to the
1661:
1648:, and others to a higher-dimensional internal space. However, there is no evidence that Pauli developed the
1481:
1423:
1353:
1114:
574:
382:
377:
219:
8472:
8396:
8391:
8326:
8254:
8156:
8059:
8049:
8034:
7951:
7042:
4105:{\displaystyle \ \partial ^{\mu }F_{\mu \nu }^{a}+g\ f^{abc}\ A^{b\mu }\ F_{\mu \nu }^{c}=-J_{\nu }^{a}~.}
1854:
Yang–Mills theories are special examples of gauge theories with a non-abelian symmetry group given by the
1485:
1239:
984:
964:
454:
387:
284:
244:
8207:
8110:
8019:
2869:
8445:
8440:
8279:
8274:
8064:
6851:
6843:
2234:
of the Lie algebra (totally antisymmetric if the generators of the Lie algebra are normalised such that
1477:
1227:
1205:
869:
724:
420:
357:
264:
1574:
field. The dynamics of the photon field and its interactions with matter are, in turn, governed by the
7833:
3937:
2446:
2295:
8386:
8120:
7956:
7927:
7664:
7610:
7540:
7392:
7184:
7161:
7113:
7050:
4205:
4125:
2329:
1290:
1280:
1119:
894:
425:
309:
259:
171:
51:
8450:
8416:
8351:
8269:
8259:
8054:
7519:
Caprini, I.; Colangelo, G.; Leutwyler, H. (2006). "Mass and width of the lowest resonance in QCD".
7194:
7027:
4298:
3766:
2856:
1129:
839:
564:
449:
7049:). The most used method to study the theory in this limit is to try to solve it on computers (see
1325:
739:
614:
8084:
7793:
7626:
7600:
7564:
7530:
7426:
7016:
6975:
2231:
1637:
1583:
1200:
in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a
1139:
1064:
994:
874:
859:
789:
749:
504:
464:
234:
196:
151:
139:
116:
111:
7759:
7644:
7240:
7074:
699:
6866:. The theory is renormalizable and corrections are finite at any order of perturbation theory.
2000:
8515:
8135:
7771:
7745:
7722:
7591:
7556:
7499:
7350:
7320:
7288:
7106:
7020:
3120:{\displaystyle \ \partial ^{\mu }F_{\mu \nu }^{a}+g\ f^{abc}\ A^{\mu b}\ F_{\mu \nu }^{c}=0~.}
2490:
1712:
1609:
1469:
1465:
1220:
1216:
1094:
1024:
909:
899:
809:
744:
679:
649:
619:
479:
474:
304:
224:
214:
106:
1819:(bottom left). A visual representation of the field strength of a BPST instanton with center
1352:
in electromagnetic fields that matched the conservation of electric charge. As the theory of
8406:
7767:
7680:
7672:
7648:
7618:
7548:
7400:
7280:
7078:
4302:
3279:
2924:), whereas for μ and ν it is nontrivial, corresponding e.g. to the usual Lorentz signature,
1791:
coefficient (top right). These coefficients determine the restriction of the BPST instanton
1665:
1599:
1587:
1134:
1049:
1029:
999:
949:
769:
759:
754:
639:
624:
554:
239:
166:
156:
91:
7477:
The problem of particle types and other contributions to the theory of elementary particles
7453:
8428:
8166:
8115:
7383:
7089:
7082:
5580:
5352:{\displaystyle S_{gf}=-{\frac {1}{2\xi }}\int \mathrm {d} ^{4}x\ (\partial \cdot A)^{2}\ }
4284:
3453:
2440:
1359:
1296:
1079:
1074:
1044:
1039:
1009:
969:
939:
919:
819:
709:
704:
669:
654:
629:
609:
589:
519:
509:
430:
392:
294:
254:
86:
64:
59:
7425:
Straumann, N. (2000). "On Pauli's invention of non-abelian Kaluza-Klein Theory in 1953".
1219:. A Yang–Mills theory seeks to describe the behavior of elementary particles using these
7668:
7614:
7544:
7396:
1464:
The idea was set aside until 1960, when the concept of particles acquiring mass through
8371:
8346:
8125:
7449:
7370:
4569:
1745:
1629:
1579:
1507:
1473:
1440:
1386:
1251:
1193:
1104:
1054:
974:
959:
944:
924:
889:
884:
879:
864:
854:
849:
814:
804:
729:
664:
634:
569:
534:
524:
499:
370:
327:
191:
8504:
8467:
8401:
8376:
7976:
7710:
7676:
7630:
7131:
4565:
1645:
1419:
1109:
1099:
1089:
1084:
1004:
989:
784:
779:
604:
599:
559:
529:
494:
484:
415:
410:
7652:
7568:
1668:. Since no such massless particles were known at the time, Shaw and his supervisor
1602:
constants it is believed they all converge to a single value at very high energies.
8411:
8321:
8039:
7981:
7966:
7268:
7166:
7058:
7038:
5579:
for the ghost. This is the expression commonly used to derive
Feynman's rules (see
4573:
1774:
1276:
1272:
1268:
1243:
1201:
1144:
1069:
954:
929:
914:
844:
764:
719:
714:
594:
584:
579:
544:
539:
514:
469:
337:
299:
121:
101:
7552:
8069:
7807:
2482:
2031:
1669:
1653:
1284:
1124:
1059:
1019:
979:
934:
794:
694:
689:
674:
659:
644:
7622:
7073:
Yang–Mills theories met with general acceptance in the physics community after
4115:
Note that the currents must properly change under gauge group transformations.
7204:
7179:
6863:
2738:
1231:
774:
684:
549:
489:
161:
96:
7292:
6965:{\displaystyle \ {\bar {c}}^{a}\ f^{abc}\ \partial _{\mu }A^{b\mu }\ c^{c}~.}
4118:
We give here some comments about the physical dimensions of the coupling. In
8202:
7718:
7284:
4313:
A method of quantizing the Yang–Mills theory is by functional methods, i.e.
2043:
1837:
1721:
1418:
In the summer 1953, Yang and Mills extended the concept of gauge theory for
1223:
7560:
7405:
7378:
4584:) that has the property of being unphysical since, although it agrees with
2426:{\displaystyle \ D_{\mu }=I\ \partial _{\mu }-i\ g\ T^{a}\ A_{\mu }^{a}\ ,}
3002:
From the given
Lagrangian one can derive the equations of motion given by
17:
8300:
7896:
7054:
1461:
This problem of unphysical massless excitation blocked further progress.
734:
7882:
7798:
5594:
7605:
7535:
7046:
7026:
is small (so small nonlinearities), as for high energies, and applying
1399:
7431:
1271:'s pioneering work on this project started in 1915 when his colleague
7685:
1571:
7092:. Furthermore, the field of Yang–Mills theories was included in the
7015:
One of the most important results obtained for Yang–Mills theory is
7319:(Impression 3 ed.). Oxford, UK: Oxford University Press.
1488:(QCD). The electroweak interaction is described by the gauge group
31:
1494:
1428:
6838:
being the generating functional of the free theory. Expanding in
1812:
to this slice. The corresponding field strength centered around
1498:
Yang–Mills theory. The massless gauge bosons of the electroweak
1283:
the "gauge symmetry", by analogy to distance standardization in
7900:
7269:"Gauge theory: Historical origins and some modern developments"
7379:"Conservation of isotopic spin and isotopic gauge invariance"
7496:
Cosmic Anger: Abdus Salam – the first Muslim Nobel scientist
7267:
O’Raifeartaigh, Lochlainn; Straumann, Norbert (2000-01-01).
5593:
3654:{\displaystyle \ \left\right]+\left\right]+\left\right]=0\ }
1873:
1660:
In
January 1954 Ronald Shaw, a graduate student at the
1279:) to quantum mechanics. Weyl named the relevant symmetry in
7792:
Svetlichny, George (1999). "Preparation for Gauge Theory".
3268:{\displaystyle \ \left(D^{\mu }F_{\mu \nu }\right)^{a}=0~.}
1410:"During the academic year 1953–1954, Yang was a visitor to
1192:
is a quantum field theory for nuclear binding devised by
2844:{\displaystyle \ \left=-i\ g\ T^{a}\ F_{\mu \nu }^{a}~.}
6858:-point functions the corresponding process amplitudes,
3758:{\displaystyle \ \left=D_{\mu }\ F_{\nu \kappa }^{a}~.}
3193:{\displaystyle \ F_{\mu \nu }=T^{a}F_{\mu \nu }^{a}\ ,}
2993:{\displaystyle \ \eta _{\mu \nu }={\rm {diag}}(+---)~.}
1586:
with the unified electroweak interaction (unifying the
1457:
quantum, to which we do not have a satisfactory answer.
1250:). Thus it forms the basis of the understanding of the
6679:
5166:
4384:
4160:
3805:
2102:
1936:
1896:
7349:. Springer Science & Business Media. p. 63.
6978:
6875:
6484:
5610:
5371:
5268:
5148:
4601:
4330:
4208:
4128:
3981:
3940:
3924:{\displaystyle \ D_{\mu }{\tilde {F}}^{\mu \nu }=0~.}
3873:
3775:
3670:
3464:
3291:
3209:
3136:
3011:
2930:
2872:
2749:
2582:
2511:
2449:
2341:
2298:
2285:{\displaystyle \ \operatorname {tr} (T^{a}\ T^{b})\ }
2240:
2055:
2003:
1866:
1443:
1362:
1328:
1299:
7653:"Regularization and renormalization of gauge fields"
7498:. Oxford, UK: Oxford University Press. p. 117.
8364:
8314:
8293:
8242:
8216:
8180:
8144:
8093:
8012:
8005:
7934:
7190:
Field theoretical formulation of the standard model
7019:. This result can be obtained by assuming that the
4588:, it is a complex scalar field, which violates the
4287:for dimensions greater than four. Furthermore, for
1468:in massless theories was put forward, initially by
7003:
6972:For the abelian case, all the structure constants
6964:
6827:
6464:
5568:
5351:
5248:
5128:
4553:
4275:
4194:
4104:
3964:
3923:
3856:
3757:
3653:
3441:
3267:
3192:
3119:
2992:
2916:
2843:
2726:
2563:
2473:
2425:
2320:
2284:
2215:
2022:
1986:
1836:(bottom right). The BPST instanton is a classical
1449:
1393:Yang and Mills find the nuclear force gauge theory
1389:in particular was obsessed with this possibility.
1377:
1344:
1314:
7109:property in the presence of additional fermions.
6850:-point functions with perturbation theory. Using
4886:
4720:
7454:"Ronald Shaw 1929–2016 by Michael Atiyah (1954)"
7343:Mathematical Conversations: Selections from the
4592:. So, we can write the generating functional as
1437:We next come to the question of the mass of the
7317:The Quantum Story: A history in 40 moments
7262:
7260:
1435:
3864:then the Bianchi identity can be rewritten as
7912:
4317:. One introduces a generating functional for
1578:gauge theory of quantum electrodynamics. The
1426:, to non-abelian groups, selecting the group
1226:and is at the core of the unification of the
1170:
8:
2493:. In four dimensions, the coupling constant
7738:Gauge Theory of Elementary Particle Physics
7420:
7418:
7416:
7310:
7308:
7306:
7304:
7302:
4283:This implies that Yang–Mills theory is not
1640:, extending the five-dimensional theory of
1624:Parallel work on non-Abelian gauge theories
8009:
7919:
7905:
7897:
7340:Gray, Jeremy; Wilson, Robin (2012-12-06).
1177:
1163:
58:
47:
7812:"Gauge theory – Past, Present and Future"
7797:
7684:
7604:
7534:
7430:
7404:
6986:
6977:
6950:
6934:
6924:
6905:
6892:
6881:
6880:
6874:
6802:
6797:
6760:
6738:
6733:
6717:
6712:
6699:
6694:
6678:
6647:
6616:
6594:
6583:
6582:
6569:
6564:
6551:
6546:
6505:
6504:
6489:
6483:
6438:
6437:
6422:
6379:
6355:
6334:
6310:
6289:
6284:
6260:
6239:
6234:
6210:
6198:
6179:
6163:
6158:
6143:
6137:
6079:
6055:
6034:
6029:
6005:
5987:
5982:
5958:
5952:
5936:
5920:
5915:
5854:
5830:
5809:
5804:
5780:
5771:
5755:
5730:
5719:
5718:
5699:
5687:
5682:
5628:
5627:
5611:
5609:
5552:
5536:
5523:
5504:
5491:
5480:
5479:
5463:
5453:
5443:
5430:
5419:
5418:
5400:
5395:
5379:
5370:
5340:
5312:
5307:
5288:
5273:
5267:
5229:
5213:
5186:
5181:
5165:
5153:
5147:
5097:
5075:
5064:
5063:
5044:
5022:
5011:
5010:
4992:
4987:
4959:
4940:
4935:
4919:
4914:
4885:
4884:
4862:
4861:
4841:
4840:
4817:
4779:
4735:
4719:
4718:
4695:
4678:
4677:
4669:
4652:
4619:
4618:
4602:
4600:
4522:
4500:
4495:
4479:
4474:
4447:
4431:
4404:
4399:
4383:
4355:
4329:
4241:
4220:
4207:
4159:
4154:
4127:
4090:
4085:
4069:
4061:
4045:
4026:
4007:
3999:
3989:
3980:
3953:
3948:
3939:
3900:
3889:
3888:
3881:
3872:
3839:
3820:
3804:
3792:
3781:
3780:
3774:
3743:
3735:
3722:
3704:
3696:
3683:
3669:
3626:
3613:
3595:
3567:
3554:
3536:
3508:
3495:
3477:
3463:
3424:
3410:
3397:
3378:
3364:
3351:
3332:
3318:
3305:
3290:
3247:
3233:
3223:
3208:
3178:
3170:
3160:
3144:
3135:
3099:
3091:
3075:
3056:
3037:
3029:
3019:
3010:
2951:
2950:
2938:
2929:
2899:
2880:
2871:
2829:
2821:
2808:
2775:
2762:
2748:
2715:
2710:
2697:
2692:
2673:
2654:
2649:
2639:
2626:
2621:
2611:
2598:
2590:
2581:
2564:{\displaystyle \ a,b,c=1\ldots n^{2}-1~.}
2543:
2510:
2462:
2457:
2448:
2411:
2406:
2393:
2368:
2349:
2340:
2306:
2297:
2270:
2257:
2239:
2201:
2182:
2158:
2142:
2117:
2101:
2087:
2074:
2054:
2011:
2002:
1975:
1967:
1951:
1935:
1920:
1895:
1879:
1878:
1872:
1871:
1865:
1442:
1361:
1333:
1327:
1298:
4554:{\displaystyle \ Z=\int \ \exp \left\ ,}
7232:
7137:Deformed Hermitian Yang–Mills equations
3972:enters into the equations of motion as
2443:(matching the size of the generators),
1632:formulated a six-dimensional theory of
1356:developed in the 1930's and 1940's the
50:
7997:Two-dimensional conformal field theory
7444:
7442:
1628:In 1953, in a private correspondence,
7:
7175:= 4 supersymmetric Yang–Mills theory
7589:(600) pole and scattering length".
2917:{\displaystyle \ f^{abc}=f_{abc}\ }
2046:or field-strength form) satisfying
1258:History and qualitative description
43:(more unsolved problems in physics)
7764:50 Years of Yang–Mills theory
6921:
6713:
6695:
6565:
6547:
6159:
5949:
5916:
5768:
5683:
5520:
5450:
5440:
5396:
5327:
5308:
5182:
4988:
4915:
4837:
4828:
4793:
4749:
4696:
4670:
4653:
4475:
4400:
4356:
4202:and so the coupling must scale as
3986:
3016:
2961:
2958:
2955:
2952:
2636:
2608:
2365:
1883:
1880:
27:In physics, a quantum field theory
25:
8492:Template:Quantum mechanics topics
7215:Yang–Mills existence and mass gap
7200:Two-dimensional Yang–Mills theory
1614:Yang–Mills existence and mass gap
8487:
8486:
7736:Cheng, T.-P.; Li, L.-F. (1983).
6846:, we are able to obtain all the
4122:dimensions, the field scales as
3965:{\displaystyle \ J_{\mu }^{a}\ }
2474:{\displaystyle \ A_{\mu }^{a}\ }
2321:{\displaystyle \ \delta ^{ab}\ }
1720:
1711:
1700:
1691:
1570:) as well as the still-massless
7875:"The Millennium Prize Problems"
7475:Shaw, Ronald (September 1956).
7241:"Yang-Mills & The Mass Gap"
6414:
6413:
6412:
6113:
6112:
5884:
4301:. So, these theories share the
4276:{\displaystyle \ \left=\left~.}
4195:{\displaystyle \ \left=\left\ }
2132:
1263:Gauge theory in electrodynamics
7152:Hermitian Yang–Mills equations
6886:
6814:
6808:
6787:
6775:
6750:
6744:
6659:
6653:
6637:
6625:
6606:
6600:
6588:
6522:
6510:
6495:
6455:
6443:
6428:
6394:
6388:
6349:
6343:
6301:
6295:
6251:
6245:
6094:
6088:
6046:
6040:
5999:
5993:
5866:
5860:
5821:
5815:
5742:
5736:
5724:
5645:
5633:
5618:
5485:
5424:
5337:
5324:
5109:
5103:
5087:
5081:
5069:
5056:
5050:
5034:
5028:
5016:
4974:
4968:
4952:
4946:
4867:
4846:
4706:
4692:
4689:
4683:
4666:
4663:
4649:
4636:
4624:
4609:
4537:
4531:
4512:
4506:
4363:
4352:
4343:
4337:
3894:
3786:
2981:
2966:
2276:
2250:
1926:
1913:
1412:Brookhaven National Laboratory
1372:
1366:
1309:
1303:
358:Renormalization group equation
1:
7553:10.1103/PhysRevLett.96.132001
7483:. ch. 3, pp. 34–46.
7458:Trinity College Annual Record
1594:) through the symmetry group
1504:spontaneous symmetry breaking
1406:. As Mills himself describes:
187:Spontaneous symmetry breaking
147:Symmetry in quantum mechanics
7677:10.1016/0550-3213(72)90279-9
1345:{\displaystyle e^{i\theta }}
8456:Quantum information science
7839:Encyclopedia of Mathematics
7004:{\displaystyle \ f^{abc}\ }
4576:with the introduction of a
3452:which is equivalent to the
2859:with small nonlinearities.
2497:is a pure number and for a
1592:electromagnetic interaction
34:Unsolved problem in physics
8532:
7879:Clay Mathematics Institute
7623:10.1103/PhysRevD.76.074034
7345:Mathematical Intelligencer
7245:Clay Mathematics Institute
7220:Yang–Mills–Higgs equations
7147:Gauge theory (mathematics)
7142:Gauge covariant derivative
7094:Clay Mathematics Institute
5587:for the ghost field while
3200:these can be rewritten as
1680:
1634:Einstein's field equations
182:Explicit symmetry breaking
8481:
7359:– via Google Books.
7273:Reviews of Modern Physics
7098:Millennium Prize Problems
7032:deep inelastic scattering
5362:for the gauge fixing and
2023:{\displaystyle \ T^{a}\ }
1510:of the weak interaction (
348:Bargmann–Wigner equations
275:Path Integral Formulation
4305:at the classical level.
1618:Millennium Prize Problem
1508:the three massive bosons
1215:, or more generally any
353:Schwinger-Dyson equation
8152:2D free massless scalar
8045:Quantum electrodynamics
7972:QFT in curved spacetime
7742:Oxford University Press
7522:Physical Review Letters
7494:Fraser, Gordon (2008).
7481:University of Cambridge
7285:10.1103/RevModPhys.72.1
4590:spin–statistics theorem
2038:, corresponding to the
1662:University of Cambridge
1600:running of the coupling
1482:electroweak unification
1424:quantum electrodynamics
1354:quantum electrodynamics
1322:produced a phase shift
383:Electroweak interaction
378:Quantum electrodynamics
343:Wheeler–DeWitt equation
220:Background field method
8473:Quantum thermodynamics
8397:On shell and off shell
8392:Loop quantum cosmology
8234:N = 4 super Yang–Mills
8193:N = 1 super Yang–Mills
8060:Scalar electrodynamics
8050:Quantum chromodynamics
7952:Conformal field theory
7928:Quantum field theories
7406:10.1103/PhysRev.96.191
7315:Baggott, J.E. (2013).
7114:lattice gauge theories
7005:
6966:
6844:functional derivatives
6829:
6466:
5598:
5570:
5353:
5250:
5130:
4586:Fermi–Dirac statistics
4555:
4277:
4196:
4106:
3966:
3925:
3858:
3759:
3655:
3443:
3269:
3194:
3121:
2994:
2918:
2845:
2737:can be derived by the
2728:
2565:
2475:
2427:
2322:
2286:
2217:
2024:
1988:
1486:quantum chromodynamics
1459:
1451:
1416:
1379:
1346:
1316:
1240:quantum chromodynamics
388:Quantum chromodynamics
245:Effective field theory
8446:Quantum hydrodynamics
8441:Quantum hadrodynamics
8065:Scalar chromodynamics
7006:
6967:
6852:LSZ reduction formula
6830:
6467:
5597:
5571:
5354:
5251:
5131:
4556:
4278:
4197:
4107:
3967:
3926:
3859:
3760:
3656:
3444:
3270:
3195:
3122:
2995:
2919:
2846:
2729:
2566:
2476:
2428:
2323:
2287:
2218:
2025:
1989:
1677:Mathematical overview
1478:Giovanni Jona-Lasinio
1452:
1408:
1380:
1347:
1317:
1254:of particle physics.
1228:electromagnetic force
1206:special unitary group
333:Klein–Gordon equation
265:LSZ reduction formula
8417:Quantum fluctuations
8387:Loop quantum gravity
7957:Lattice field theory
7715:Gauge Field Theories
7210:Yang–Mills equations
7185:Quantum gauge theory
7162:Lattice gauge theory
7127:Aharonov–Bohm effect
7051:lattice gauge theory
6976:
6873:
6482:
5608:
5369:
5266:
5146:
4599:
4328:
4321:-point functions as
4206:
4126:
3979:
3938:
3871:
3773:
3668:
3462:
3289:
3207:
3134:
3009:
2928:
2870:
2747:
2580:
2509:
2447:
2339:
2330:covariant derivative
2296:
2238:
2053:
2001:
1997:with the generators
1864:
1842:Yang–Mills equations
1683:Yang–Mills equations
1596:SU(3) × SU(2) × U(1)
1441:
1378:{\displaystyle U(1)}
1360:
1326:
1315:{\displaystyle U(1)}
1297:
1242:, the theory of the
426:Theory of everything
260:Lattice field theory
230:Correlation function
52:Quantum field theory
8451:Quantum information
8055:Quartic interaction
7852:"Yang–Mills theory"
7669:1972NuPhB..44..189T
7615:2007PhRvD..76g4034G
7545:2006PhRvL..96m2001C
7397:1954PhRv...96..191Y
7195:Symmetry in physics
7157:Kaluza–Klein theory
7028:perturbation theory
6807:
6743:
6294:
6244:
6039:
5992:
5814:
4945:
4582:Faddeev–Popov ghost
4505:
4299:scalar field theory
4095:
4074:
4012:
3958:
3748:
3709:
3183:
3104:
3042:
2857:perturbation theory
2834:
2720:
2702:
2659:
2631:
2603:
2467:
2416:
2292:is proportional to
2232:structure constants
1980:
405:Incomplete theories
8337:Nambu–Jona-Lasinio
8265:Higher dimensional
8172:Wess–Zumino–Witten
7962:Noncommutative QFT
7834:"Yang-Mills field"
7017:asymptotic freedom
7001:
6962:
6842:and computing the
6825:
6793:
6729:
6688:
6462:
6460:
6280:
6230:
6025:
5978:
5800:
5599:
5566:
5349:
5246:
5175:
5126:
5124:
4931:
4551:
4491:
4393:
4273:
4192:
4177:
4102:
4081:
4057:
3995:
3962:
3944:
3921:
3854:
3814:
3755:
3731:
3692:
3651:
3439:
3265:
3190:
3166:
3117:
3087:
3025:
2990:
2914:
2841:
2817:
2724:
2706:
2688:
2645:
2617:
2586:
2561:
2471:
2453:
2423:
2402:
2318:
2282:
2213:
2111:
2020:
1984:
1963:
1945:
1905:
1638:general relativity
1584:strong interaction
1492:, while QCD is an
1447:
1375:
1342:
1312:
270:Partition function
197:Topological charge
117:General relativity
112:Special relativity
8498:
8497:
8360:
8359:
7760:'t Hooft, G.
7728:978-3-527-40835-1
7657:Nuclear Physics B
7645:'t Hooft, G.
7592:Physical Review D
7326:978-0-19-956684-6
7102:the prize-problem
7043:ultraviolet limit
7021:coupling constant
7000:
6981:
6958:
6945:
6919:
6900:
6889:
6878:
6824:
6792:
6755:
6728:
6710:
6687:
6642:
6611:
6591:
6580:
6562:
6513:
6446:
6398:
6374:
6363:
6353:
6329:
6315:
6309:
6305:
6279:
6268:
6259:
6255:
6229:
6218:
6193:
6174:
6152:
6136:
6098:
6074:
6063:
6054:
6050:
6024:
6013:
6003:
5977:
5966:
5931:
5907:
5870:
5849:
5838:
5829:
5825:
5799:
5788:
5779:
5750:
5746:
5727:
5716:
5710:
5698:
5674:
5636:
5565:
5547:
5531:
5518:
5499:
5488:
5477:
5438:
5427:
5411:
5374:
5348:
5323:
5301:
5245:
5224:
5197:
5174:
5092:
5072:
5039:
5019:
5003:
4930:
4870:
4849:
4812:
4774:
4743:
4730:
4711:
4702:
4686:
4676:
4659:
4627:
4547:
4517:
4490:
4469:
4442:
4415:
4392:
4368:
4333:
4269:
4211:
4191:
4176:
4131:
4098:
4056:
4040:
4021:
3984:
3961:
3943:
3917:
3897:
3876:
3850:
3813:
3789:
3778:
3751:
3730:
3673:
3650:
3467:
3438:
3405:
3359:
3313:
3294:
3261:
3212:
3186:
3139:
3113:
3086:
3070:
3051:
3014:
2986:
2933:
2913:
2875:
2837:
2816:
2803:
2797:
2752:
2723:
2705:
2687:
2668:
2585:
2557:
2514:
2491:coupling constant
2470:
2452:
2419:
2401:
2388:
2382:
2363:
2344:
2317:
2301:
2281:
2265:
2243:
2209:
2196:
2177:
2153:
2128:
2110:
2082:
2058:
2042:-quantities (the
2019:
2006:
1983:
1944:
1904:
1869:
1744:coefficient of a
1470:Jeffrey Goldstone
1466:symmetry breaking
1450:{\displaystyle b}
1291:Erwin Schrödinger
1281:Noether's theorem
1217:compact Lie group
1190:Yang–Mills theory
1187:
1186:
250:Expectation value
225:BRST quantization
172:Poincaré symmetry
127:Yang–Mills theory
107:Quantum mechanics
16:(Redirected from
8523:
8490:
8489:
8407:Quantum dynamics
8080:Yang–Mills–Higgs
8035:Non-linear sigma
8025:Euler–Heisenberg
8010:
7921:
7914:
7907:
7898:
7893:
7891:
7890:
7881:. Archived from
7870:
7868:
7867:
7858:. Archived from
7847:
7821:
7819:
7818:
7803:
7801:
7781:
7768:World Scientific
7755:
7732:
7717:(3rd ed.).
7691:
7690:
7688:
7641:
7635:
7634:
7608:
7585:
7579:
7573:
7572:
7538:
7516:
7510:
7509:
7491:
7485:
7484:
7479:(Ph.D. thesis).
7472:
7466:
7465:
7446:
7437:
7436:
7434:
7422:
7411:
7410:
7408:
7367:
7361:
7360:
7337:
7331:
7330:
7312:
7297:
7296:
7264:
7255:
7254:
7252:
7251:
7237:
7174:
7079:Martinus Veltman
7064:
7025:
7010:
7008:
7007:
7002:
6998:
6997:
6996:
6979:
6971:
6969:
6968:
6963:
6956:
6955:
6954:
6943:
6942:
6941:
6929:
6928:
6917:
6916:
6915:
6898:
6897:
6896:
6891:
6890:
6882:
6876:
6857:
6854:we get from the
6849:
6841:
6834:
6832:
6831:
6826:
6822:
6821:
6817:
6806:
6801:
6790:
6774:
6773:
6753:
6742:
6737:
6726:
6722:
6721:
6716:
6708:
6704:
6703:
6698:
6689:
6680:
6666:
6662:
6652:
6651:
6640:
6624:
6623:
6609:
6599:
6598:
6593:
6592:
6584:
6578:
6574:
6573:
6568:
6560:
6556:
6555:
6550:
6515:
6514:
6506:
6494:
6493:
6471:
6469:
6468:
6463:
6461:
6448:
6447:
6439:
6427:
6426:
6408:
6404:
6400:
6399:
6397:
6387:
6386:
6372:
6367:
6361:
6356:
6354:
6352:
6342:
6341:
6327:
6322:
6313:
6311:
6307:
6306:
6304:
6293:
6288:
6277:
6272:
6266:
6261:
6257:
6256:
6254:
6243:
6238:
6227:
6222:
6216:
6211:
6209:
6208:
6191:
6190:
6189:
6172:
6168:
6167:
6162:
6153:
6148:
6147:
6138:
6134:
6108:
6104:
6100:
6099:
6097:
6087:
6086:
6072:
6067:
6061:
6056:
6052:
6051:
6049:
6038:
6033:
6022:
6017:
6011:
6006:
6004:
6002:
5991:
5986:
5975:
5970:
5964:
5959:
5957:
5956:
5947:
5946:
5929:
5925:
5924:
5919:
5905:
5880:
5876:
5872:
5871:
5869:
5859:
5858:
5847:
5842:
5836:
5831:
5827:
5826:
5824:
5813:
5808:
5797:
5792:
5786:
5781:
5777:
5776:
5775:
5766:
5765:
5748:
5747:
5745:
5735:
5734:
5729:
5728:
5720:
5714:
5708:
5700:
5696:
5692:
5691:
5686:
5672:
5638:
5637:
5629:
5590:
5586:
5583:). Here we have
5575:
5573:
5572:
5567:
5563:
5562:
5558:
5557:
5556:
5545:
5544:
5543:
5529:
5528:
5527:
5516:
5515:
5514:
5497:
5496:
5495:
5490:
5489:
5481:
5475:
5468:
5467:
5458:
5457:
5448:
5447:
5436:
5435:
5434:
5429:
5428:
5420:
5409:
5405:
5404:
5399:
5384:
5383:
5372:
5358:
5356:
5355:
5350:
5346:
5345:
5344:
5321:
5317:
5316:
5311:
5302:
5300:
5289:
5281:
5280:
5255:
5253:
5252:
5247:
5243:
5242:
5238:
5237:
5236:
5222:
5221:
5220:
5195:
5191:
5190:
5185:
5176:
5167:
5158:
5157:
5135:
5133:
5132:
5127:
5125:
5121:
5117:
5116:
5112:
5102:
5101:
5090:
5080:
5079:
5074:
5073:
5065:
5049:
5048:
5037:
5027:
5026:
5021:
5020:
5012:
5001:
4997:
4996:
4991:
4967:
4966:
4944:
4939:
4928:
4924:
4923:
4918:
4894:
4890:
4889:
4883:
4879:
4872:
4871:
4863:
4851:
4850:
4842:
4822:
4821:
4810:
4803:
4799:
4787:
4786:
4772:
4765:
4761:
4741:
4740:
4739:
4728:
4724:
4723:
4709:
4700:
4699:
4688:
4687:
4679:
4674:
4673:
4657:
4656:
4629:
4628:
4620:
4560:
4558:
4557:
4552:
4545:
4544:
4540:
4530:
4529:
4515:
4504:
4499:
4488:
4484:
4483:
4478:
4467:
4460:
4456:
4455:
4454:
4440:
4439:
4438:
4413:
4409:
4408:
4403:
4394:
4385:
4366:
4359:
4331:
4320:
4303:scale invariance
4296:
4294:
4282:
4280:
4279:
4274:
4267:
4266:
4262:
4261:
4260:
4256:
4229:
4225:
4224:
4209:
4201:
4199:
4198:
4193:
4189:
4188:
4184:
4183:
4182:
4178:
4172:
4161:
4142:
4129:
4121:
4111:
4109:
4108:
4103:
4096:
4094:
4089:
4073:
4068:
4054:
4053:
4052:
4038:
4037:
4036:
4019:
4011:
4006:
3994:
3993:
3982:
3971:
3969:
3968:
3963:
3959:
3957:
3952:
3941:
3930:
3928:
3927:
3922:
3915:
3908:
3907:
3899:
3898:
3890:
3886:
3885:
3874:
3863:
3861:
3860:
3855:
3848:
3847:
3846:
3834:
3833:
3815:
3806:
3800:
3799:
3791:
3790:
3782:
3776:
3769:strength tensor
3764:
3762:
3761:
3756:
3749:
3747:
3742:
3728:
3727:
3726:
3714:
3710:
3708:
3703:
3688:
3687:
3671:
3660:
3658:
3657:
3652:
3648:
3641:
3637:
3636:
3632:
3631:
3630:
3618:
3617:
3600:
3599:
3582:
3578:
3577:
3573:
3572:
3571:
3559:
3558:
3541:
3540:
3523:
3519:
3518:
3514:
3513:
3512:
3500:
3499:
3482:
3481:
3465:
3448:
3446:
3445:
3440:
3436:
3429:
3428:
3423:
3419:
3418:
3417:
3403:
3402:
3401:
3383:
3382:
3377:
3373:
3372:
3371:
3357:
3356:
3355:
3337:
3336:
3331:
3327:
3326:
3325:
3311:
3310:
3309:
3292:
3280:Bianchi identity
3274:
3272:
3271:
3266:
3259:
3252:
3251:
3246:
3242:
3241:
3240:
3228:
3227:
3210:
3199:
3197:
3196:
3191:
3184:
3182:
3177:
3165:
3164:
3152:
3151:
3137:
3126:
3124:
3123:
3118:
3111:
3103:
3098:
3084:
3083:
3082:
3068:
3067:
3066:
3049:
3041:
3036:
3024:
3023:
3012:
2999:
2997:
2996:
2991:
2984:
2965:
2964:
2946:
2945:
2931:
2923:
2921:
2920:
2915:
2911:
2910:
2909:
2891:
2890:
2873:
2850:
2848:
2847:
2842:
2835:
2833:
2828:
2814:
2813:
2812:
2801:
2795:
2785:
2781:
2780:
2779:
2767:
2766:
2750:
2733:
2731:
2730:
2725:
2721:
2719:
2714:
2703:
2701:
2696:
2685:
2684:
2683:
2666:
2658:
2653:
2644:
2643:
2630:
2625:
2616:
2615:
2602:
2597:
2583:
2570:
2568:
2567:
2562:
2555:
2548:
2547:
2512:
2504:
2496:
2488:
2480:
2478:
2477:
2472:
2468:
2466:
2461:
2450:
2438:
2432:
2430:
2429:
2424:
2417:
2415:
2410:
2399:
2398:
2397:
2386:
2380:
2373:
2372:
2361:
2354:
2353:
2342:
2327:
2325:
2324:
2319:
2315:
2314:
2313:
2299:
2291:
2289:
2288:
2283:
2279:
2275:
2274:
2263:
2262:
2261:
2241:
2229:
2222:
2220:
2219:
2214:
2207:
2206:
2205:
2194:
2193:
2192:
2175:
2168:
2164:
2163:
2162:
2151:
2147:
2146:
2126:
2125:
2124:
2112:
2103:
2097:
2093:
2092:
2091:
2080:
2079:
2078:
2056:
2041:
2037:
2029:
2027:
2026:
2021:
2017:
2016:
2015:
2004:
1993:
1991:
1990:
1985:
1981:
1979:
1974:
1962:
1961:
1946:
1937:
1925:
1924:
1906:
1897:
1888:
1887:
1886:
1877:
1876:
1867:
1847:
1840:solution to the
1835:
1831:
1825:compactification
1822:
1818:
1811:
1810:
1794:
1790:
1777:(top left). The
1772:
1763:
1759:
1743:
1724:
1715:
1704:
1695:
1666:gauge invariance
1597:
1577:
1569:
1568:
1567:
1566:
1559:
1558:
1549:
1548:
1547:
1546:
1539:
1538:
1529:
1528:
1527:
1526:
1519:
1518:
1501:
1497:
1491:
1456:
1454:
1453:
1448:
1431:
1384:
1382:
1381:
1376:
1351:
1349:
1348:
1343:
1341:
1340:
1321:
1319:
1318:
1313:
1249:
1237:
1214:
1179:
1172:
1165:
240:Effective action
167:Lorentz symmetry
92:Electromagnetism
62:
48:
35:
21:
8531:
8530:
8526:
8525:
8524:
8522:
8521:
8520:
8501:
8500:
8499:
8494:
8477:
8429:Quantum gravity
8356:
8315:Particle theory
8310:
8289:
8238:
8212:
8176:
8140:
8094:Low dimensional
8089:
8030:Ginzburg–Landau
8001:
7992:Topological QFT
7930:
7925:
7888:
7886:
7873:
7865:
7863:
7850:
7832:
7829:
7824:
7816:
7814:
7806:
7799:math-ph/9902027
7791:
7778:
7758:
7752:
7735:
7729:
7709:
7700:
7698:Further reading
7695:
7694:
7643:
7642:
7638:
7588:
7583:
7581:
7580:
7576:
7518:
7517:
7513:
7506:
7493:
7492:
7488:
7474:
7473:
7469:
7448:
7447:
7440:
7424:
7423:
7414:
7384:Physical Review
7369:
7368:
7364:
7357:
7339:
7338:
7334:
7327:
7314:
7313:
7300:
7266:
7265:
7258:
7249:
7247:
7239:
7238:
7234:
7229:
7224:
7172:
7122:
7090:Simon Donaldson
7083:Higgs mechanism
7075:Gerard 't Hooft
7071:
7062:
7023:
6982:
6974:
6973:
6946:
6930:
6920:
6901:
6879:
6871:
6870:
6855:
6847:
6839:
6756:
6711:
6693:
6677:
6673:
6643:
6612:
6581:
6563:
6545:
6538:
6534:
6485:
6480:
6479:
6459:
6458:
6418:
6406:
6405:
6375:
6368:
6357:
6330:
6323:
6312:
6273:
6262:
6223:
6212:
6194:
6175:
6157:
6139:
6127:
6123:
6106:
6105:
6075:
6068:
6057:
6018:
6007:
5971:
5960:
5948:
5932:
5914:
5898:
5894:
5878:
5877:
5850:
5843:
5832:
5793:
5782:
5767:
5751:
5717:
5704:
5681:
5665:
5661:
5648:
5606:
5605:
5588:
5584:
5581:Feynman diagram
5548:
5532:
5519:
5500:
5478:
5459:
5449:
5439:
5417:
5416:
5412:
5394:
5375:
5367:
5366:
5336:
5306:
5293:
5269:
5264:
5263:
5259:for the field,
5225:
5209:
5208:
5204:
5180:
5149:
5144:
5143:
5123:
5122:
5093:
5062:
5040:
5009:
5008:
5004:
4986:
4955:
4913:
4906:
4902:
4892:
4891:
4827:
4823:
4813:
4792:
4788:
4775:
4748:
4744:
4731:
4639:
4597:
4596:
4518:
4473:
4443:
4427:
4426:
4422:
4398:
4379:
4375:
4326:
4325:
4318:
4311:
4289:
4288:
4246:
4242:
4237:
4233:
4216:
4212:
4204:
4203:
4162:
4155:
4150:
4146:
4132:
4124:
4123:
4119:
4041:
4022:
3985:
3977:
3976:
3936:
3935:
3887:
3877:
3869:
3868:
3835:
3816:
3779:
3771:
3770:
3718:
3679:
3678:
3674:
3666:
3665:
3622:
3609:
3608:
3604:
3591:
3590:
3586:
3563:
3550:
3549:
3545:
3532:
3531:
3527:
3504:
3491:
3490:
3486:
3473:
3472:
3468:
3460:
3459:
3454:Jacobi identity
3406:
3393:
3392:
3388:
3387:
3360:
3347:
3346:
3342:
3341:
3314:
3301:
3300:
3296:
3295:
3287:
3286:
3229:
3219:
3218:
3214:
3213:
3205:
3204:
3156:
3140:
3132:
3131:
3071:
3052:
3015:
3007:
3006:
2934:
2926:
2925:
2895:
2876:
2868:
2867:
2804:
2771:
2758:
2757:
2753:
2745:
2744:
2669:
2635:
2607:
2578:
2577:
2539:
2507:
2506:
2498:
2494:
2486:
2485:potential, and
2445:
2444:
2441:identity matrix
2436:
2389:
2364:
2345:
2337:
2336:
2302:
2294:
2293:
2266:
2253:
2236:
2235:
2227:
2197:
2178:
2154:
2138:
2137:
2133:
2113:
2083:
2070:
2069:
2065:
2051:
2050:
2039:
2035:
2007:
1999:
1998:
1947:
1916:
1870:
1862:
1861:
1852:
1851:
1850:
1849:
1845:
1833:
1827:
1820:
1813:
1797:
1796:
1792:
1789:
1778:
1771:
1765:
1761:
1749:
1742:
1731:
1727:
1726:
1725:
1717:
1716:
1707:
1706:
1705:
1697:
1696:
1685:
1679:
1626:
1595:
1575:
1565:
1563:
1562:
1561:
1557:
1555:
1554:
1553:
1552:
1551:
1545:
1543:
1542:
1541:
1537:
1535:
1534:
1533:
1532:
1531:
1525:
1523:
1522:
1521:
1517:
1515:
1514:
1513:
1512:
1511:
1499:
1493:
1489:
1439:
1438:
1427:
1395:
1358:
1357:
1329:
1324:
1323:
1295:
1294:
1285:railroad gauges
1265:
1260:
1247:
1235:
1208:
1183:
1154:
1153:
1152:
1150:
444:
436:
435:
431:Quantum gravity
406:
398:
397:
393:Higgs mechanism
373:
363:
362:
338:Proca equations
323:
315:
314:
310:Wightman Axioms
295:Renormalization
255:Feynman diagram
210:
202:
201:
142:
132:
131:
82:
67:
65:Feynman diagram
46:
45:
40:
37:
33:
28:
23:
22:
15:
12:
11:
5:
8529:
8527:
8519:
8518:
8513:
8511:Gauge theories
8503:
8502:
8496:
8495:
8482:
8479:
8478:
8476:
8475:
8470:
8465:
8464:
8463:
8453:
8448:
8443:
8438:
8437:
8436:
8426:
8425:
8424:
8414:
8409:
8404:
8399:
8394:
8389:
8384:
8379:
8374:
8372:Casimir effect
8368:
8366:
8362:
8361:
8358:
8357:
8355:
8354:
8349:
8347:Standard Model
8344:
8339:
8334:
8329:
8324:
8318:
8316:
8312:
8311:
8309:
8308:
8303:
8297:
8295:
8291:
8290:
8288:
8287:
8282:
8277:
8272:
8267:
8262:
8257:
8252:
8246:
8244:
8240:
8239:
8237:
8236:
8231:
8226:
8220:
8218:
8217:Superconformal
8214:
8213:
8211:
8210:
8205:
8200:
8198:Seiberg–Witten
8195:
8190:
8184:
8182:
8181:Supersymmetric
8178:
8177:
8175:
8174:
8169:
8164:
8159:
8154:
8148:
8146:
8142:
8141:
8139:
8138:
8133:
8128:
8123:
8118:
8113:
8108:
8103:
8097:
8095:
8091:
8090:
8088:
8087:
8082:
8077:
8072:
8067:
8062:
8057:
8052:
8047:
8042:
8037:
8032:
8027:
8022:
8016:
8014:
8007:
8003:
8002:
8000:
7999:
7994:
7989:
7984:
7979:
7974:
7969:
7964:
7959:
7954:
7949:
7944:
7938:
7936:
7932:
7931:
7926:
7924:
7923:
7916:
7909:
7901:
7895:
7894:
7871:
7856:DispersiveWiki
7848:
7828:
7827:External links
7825:
7823:
7822:
7804:
7788:
7787:
7783:
7782:
7776:
7762:, ed. (2005).
7756:
7750:
7733:
7727:
7706:
7705:
7701:
7699:
7696:
7693:
7692:
7663:(1): 189–213.
7636:
7606:hep-ph/0701025
7586:
7574:
7536:hep-ph/0512364
7529:(13): 132001.
7511:
7505:978-0199208463
7504:
7486:
7467:
7438:
7412:
7391:(1): 191–195.
7362:
7355:
7332:
7325:
7298:
7256:
7231:
7230:
7228:
7225:
7223:
7222:
7217:
7212:
7207:
7202:
7197:
7192:
7187:
7182:
7177:
7169:
7164:
7159:
7154:
7149:
7144:
7139:
7134:
7129:
7123:
7121:
7118:
7070:
7067:
6995:
6992:
6989:
6985:
6961:
6953:
6949:
6940:
6937:
6933:
6927:
6923:
6914:
6911:
6908:
6904:
6895:
6888:
6885:
6860:cross sections
6836:
6835:
6820:
6816:
6813:
6810:
6805:
6800:
6796:
6789:
6786:
6783:
6780:
6777:
6772:
6769:
6766:
6763:
6759:
6752:
6749:
6746:
6741:
6736:
6732:
6725:
6720:
6715:
6707:
6702:
6697:
6692:
6686:
6683:
6676:
6672:
6669:
6665:
6661:
6658:
6655:
6650:
6646:
6639:
6636:
6633:
6630:
6627:
6622:
6619:
6615:
6608:
6605:
6602:
6597:
6590:
6587:
6577:
6572:
6567:
6559:
6554:
6549:
6544:
6541:
6537:
6533:
6530:
6527:
6524:
6521:
6518:
6512:
6509:
6503:
6500:
6497:
6492:
6488:
6473:
6472:
6457:
6454:
6451:
6445:
6442:
6436:
6433:
6430:
6425:
6421:
6417:
6411:
6409:
6407:
6403:
6396:
6393:
6390:
6385:
6382:
6378:
6371:
6366:
6360:
6351:
6348:
6345:
6340:
6337:
6333:
6326:
6321:
6318:
6303:
6300:
6297:
6292:
6287:
6283:
6276:
6271:
6265:
6253:
6250:
6247:
6242:
6237:
6233:
6226:
6221:
6215:
6207:
6204:
6201:
6197:
6188:
6185:
6182:
6178:
6171:
6166:
6161:
6156:
6151:
6146:
6142:
6133:
6130:
6126:
6122:
6119:
6116:
6111:
6109:
6107:
6103:
6096:
6093:
6090:
6085:
6082:
6078:
6071:
6066:
6060:
6048:
6045:
6042:
6037:
6032:
6028:
6021:
6016:
6010:
6001:
5998:
5995:
5990:
5985:
5981:
5974:
5969:
5963:
5955:
5951:
5945:
5942:
5939:
5935:
5928:
5923:
5918:
5913:
5910:
5904:
5901:
5897:
5893:
5890:
5887:
5883:
5881:
5879:
5875:
5868:
5865:
5862:
5857:
5853:
5846:
5841:
5835:
5823:
5820:
5817:
5812:
5807:
5803:
5796:
5791:
5785:
5774:
5770:
5764:
5761:
5758:
5754:
5744:
5741:
5738:
5733:
5726:
5723:
5713:
5707:
5703:
5695:
5690:
5685:
5680:
5677:
5671:
5668:
5664:
5660:
5657:
5654:
5651:
5649:
5647:
5644:
5641:
5635:
5632:
5626:
5623:
5620:
5617:
5614:
5613:
5577:
5576:
5561:
5555:
5551:
5542:
5539:
5535:
5526:
5522:
5513:
5510:
5507:
5503:
5494:
5487:
5484:
5474:
5471:
5466:
5462:
5456:
5452:
5446:
5442:
5433:
5426:
5423:
5415:
5408:
5403:
5398:
5393:
5390:
5387:
5382:
5378:
5360:
5359:
5343:
5339:
5335:
5332:
5329:
5326:
5320:
5315:
5310:
5305:
5299:
5296:
5292:
5287:
5284:
5279:
5276:
5272:
5257:
5256:
5241:
5235:
5232:
5228:
5219:
5216:
5212:
5207:
5203:
5200:
5194:
5189:
5184:
5179:
5173:
5170:
5164:
5161:
5156:
5152:
5137:
5136:
5120:
5115:
5111:
5108:
5105:
5100:
5096:
5089:
5086:
5083:
5078:
5071:
5068:
5061:
5058:
5055:
5052:
5047:
5043:
5036:
5033:
5030:
5025:
5018:
5015:
5007:
5000:
4995:
4990:
4985:
4982:
4979:
4976:
4973:
4970:
4965:
4962:
4958:
4954:
4951:
4948:
4943:
4938:
4934:
4927:
4922:
4917:
4912:
4909:
4905:
4901:
4898:
4895:
4893:
4888:
4882:
4878:
4875:
4869:
4866:
4860:
4857:
4854:
4848:
4845:
4839:
4836:
4833:
4830:
4826:
4820:
4816:
4809:
4806:
4802:
4798:
4795:
4791:
4785:
4782:
4778:
4771:
4768:
4764:
4760:
4757:
4754:
4751:
4747:
4738:
4734:
4727:
4722:
4717:
4714:
4708:
4705:
4698:
4694:
4691:
4685:
4682:
4672:
4668:
4665:
4662:
4655:
4651:
4648:
4645:
4642:
4640:
4638:
4635:
4632:
4626:
4623:
4617:
4614:
4611:
4608:
4605:
4604:
4570:Ludvig Faddeev
4562:
4561:
4550:
4543:
4539:
4536:
4533:
4528:
4525:
4521:
4514:
4511:
4508:
4503:
4498:
4494:
4487:
4482:
4477:
4472:
4466:
4463:
4459:
4453:
4450:
4446:
4437:
4434:
4430:
4425:
4421:
4418:
4412:
4407:
4402:
4397:
4391:
4388:
4382:
4378:
4374:
4371:
4365:
4362:
4358:
4354:
4351:
4348:
4345:
4342:
4339:
4336:
4315:path integrals
4310:
4307:
4285:renormalizable
4272:
4265:
4259:
4255:
4252:
4249:
4245:
4240:
4236:
4232:
4228:
4223:
4219:
4215:
4187:
4181:
4175:
4171:
4168:
4165:
4158:
4153:
4149:
4145:
4141:
4138:
4135:
4113:
4112:
4101:
4093:
4088:
4084:
4080:
4077:
4072:
4067:
4064:
4060:
4051:
4048:
4044:
4035:
4032:
4029:
4025:
4018:
4015:
4010:
4005:
4002:
3998:
3992:
3988:
3956:
3951:
3947:
3932:
3931:
3920:
3914:
3911:
3906:
3903:
3896:
3893:
3884:
3880:
3853:
3845:
3842:
3838:
3832:
3829:
3826:
3823:
3819:
3812:
3809:
3803:
3798:
3795:
3788:
3785:
3754:
3746:
3741:
3738:
3734:
3725:
3721:
3717:
3713:
3707:
3702:
3699:
3695:
3691:
3686:
3682:
3677:
3662:
3661:
3647:
3644:
3640:
3635:
3629:
3625:
3621:
3616:
3612:
3607:
3603:
3598:
3594:
3589:
3585:
3581:
3576:
3570:
3566:
3562:
3557:
3553:
3548:
3544:
3539:
3535:
3530:
3526:
3522:
3517:
3511:
3507:
3503:
3498:
3494:
3489:
3485:
3480:
3476:
3471:
3450:
3449:
3435:
3432:
3427:
3422:
3416:
3413:
3409:
3400:
3396:
3391:
3386:
3381:
3376:
3370:
3367:
3363:
3354:
3350:
3345:
3340:
3335:
3330:
3324:
3321:
3317:
3308:
3304:
3299:
3276:
3275:
3264:
3258:
3255:
3250:
3245:
3239:
3236:
3232:
3226:
3222:
3217:
3189:
3181:
3176:
3173:
3169:
3163:
3159:
3155:
3150:
3147:
3143:
3128:
3127:
3116:
3110:
3107:
3102:
3097:
3094:
3090:
3081:
3078:
3074:
3065:
3062:
3059:
3055:
3048:
3045:
3040:
3035:
3032:
3028:
3022:
3018:
2989:
2983:
2980:
2977:
2974:
2971:
2968:
2963:
2960:
2957:
2954:
2949:
2944:
2941:
2937:
2908:
2905:
2902:
2898:
2894:
2889:
2886:
2883:
2879:
2866:indices (e.g.
2852:
2851:
2840:
2832:
2827:
2824:
2820:
2811:
2807:
2800:
2794:
2791:
2788:
2784:
2778:
2774:
2770:
2765:
2761:
2756:
2735:
2734:
2718:
2713:
2709:
2700:
2695:
2691:
2682:
2679:
2676:
2672:
2665:
2662:
2657:
2652:
2648:
2642:
2638:
2634:
2629:
2624:
2620:
2614:
2610:
2606:
2601:
2596:
2593:
2589:
2560:
2554:
2551:
2546:
2542:
2538:
2535:
2532:
2529:
2526:
2523:
2520:
2517:
2505:group one has
2465:
2460:
2456:
2434:
2433:
2422:
2414:
2409:
2405:
2396:
2392:
2385:
2379:
2376:
2371:
2367:
2360:
2357:
2352:
2348:
2332:is defined as
2312:
2309:
2305:
2278:
2273:
2269:
2260:
2256:
2252:
2249:
2246:
2224:
2223:
2212:
2204:
2200:
2191:
2188:
2185:
2181:
2174:
2171:
2167:
2161:
2157:
2150:
2145:
2141:
2136:
2131:
2123:
2120:
2116:
2109:
2106:
2100:
2096:
2090:
2086:
2077:
2073:
2068:
2064:
2061:
2014:
2010:
1995:
1994:
1978:
1973:
1970:
1966:
1960:
1957:
1954:
1950:
1943:
1940:
1934:
1931:
1928:
1923:
1919:
1915:
1912:
1909:
1903:
1900:
1894:
1891:
1885:
1882:
1875:
1787:
1769:
1746:BPST instanton
1740:
1729:
1728:
1719:
1718:
1710:
1709:
1708:
1699:
1698:
1690:
1689:
1688:
1687:
1686:
1678:
1675:
1630:Wolfgang Pauli
1625:
1622:
1580:Standard Model
1564:
1556:
1544:
1536:
1524:
1516:
1474:Yoichiro Nambu
1446:
1420:abelian groups
1394:
1391:
1387:Chen Ning Yang
1374:
1371:
1368:
1365:
1339:
1336:
1332:
1311:
1308:
1305:
1302:
1264:
1261:
1259:
1256:
1252:Standard Model
1194:Chen Ning Yang
1185:
1184:
1182:
1181:
1174:
1167:
1159:
1156:
1155:
1148:
1147:
1142:
1137:
1132:
1127:
1122:
1117:
1112:
1107:
1102:
1097:
1092:
1087:
1082:
1077:
1072:
1067:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1027:
1022:
1017:
1012:
1007:
1002:
997:
992:
987:
982:
977:
972:
967:
962:
957:
952:
947:
942:
937:
932:
927:
922:
917:
912:
907:
902:
897:
892:
887:
882:
877:
872:
867:
862:
857:
852:
847:
842:
837:
832:
827:
822:
817:
812:
807:
802:
797:
792:
787:
782:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
622:
617:
612:
607:
602:
597:
592:
587:
582:
577:
572:
567:
562:
557:
552:
547:
542:
537:
532:
527:
522:
517:
512:
507:
502:
497:
492:
487:
482:
477:
472:
467:
462:
457:
452:
446:
445:
442:
441:
438:
437:
434:
433:
428:
423:
418:
413:
407:
404:
403:
400:
399:
396:
395:
390:
385:
380:
374:
371:Standard Model
369:
368:
365:
364:
361:
360:
355:
350:
345:
340:
335:
330:
328:Dirac equation
324:
321:
320:
317:
316:
313:
312:
307:
305:Wick's theorem
302:
297:
292:
290:Regularization
287:
282:
277:
272:
267:
262:
257:
252:
247:
242:
237:
232:
227:
222:
217:
211:
208:
207:
204:
203:
200:
199:
194:
192:Noether charge
189:
184:
179:
177:Gauge symmetry
174:
169:
164:
159:
154:
149:
143:
138:
137:
134:
133:
130:
129:
124:
119:
114:
109:
104:
99:
94:
89:
83:
80:
79:
76:
75:
69:
68:
63:
55:
54:
41:
38:
32:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8528:
8517:
8514:
8512:
8509:
8508:
8506:
8493:
8485:
8480:
8474:
8471:
8469:
8468:Quantum logic
8466:
8462:
8459:
8458:
8457:
8454:
8452:
8449:
8447:
8444:
8442:
8439:
8435:
8432:
8431:
8430:
8427:
8423:
8420:
8419:
8418:
8415:
8413:
8410:
8408:
8405:
8403:
8402:Quantum chaos
8400:
8398:
8395:
8393:
8390:
8388:
8385:
8383:
8380:
8378:
8377:Cosmic string
8375:
8373:
8370:
8369:
8367:
8363:
8353:
8350:
8348:
8345:
8343:
8340:
8338:
8335:
8333:
8330:
8328:
8325:
8323:
8320:
8319:
8317:
8313:
8307:
8304:
8302:
8299:
8298:
8296:
8292:
8286:
8283:
8281:
8278:
8276:
8273:
8271:
8268:
8266:
8263:
8261:
8258:
8256:
8253:
8251:
8250:Pure 4D N = 1
8248:
8247:
8245:
8241:
8235:
8232:
8230:
8227:
8225:
8222:
8221:
8219:
8215:
8209:
8206:
8204:
8201:
8199:
8196:
8194:
8191:
8189:
8186:
8185:
8183:
8179:
8173:
8170:
8168:
8165:
8163:
8160:
8158:
8155:
8153:
8150:
8149:
8147:
8143:
8137:
8134:
8132:
8131:Thirring–Wess
8129:
8127:
8124:
8122:
8119:
8117:
8114:
8112:
8109:
8107:
8106:Bullough–Dodd
8104:
8102:
8101:2D Yang–Mills
8099:
8098:
8096:
8092:
8086:
8083:
8081:
8078:
8076:
8073:
8071:
8068:
8066:
8063:
8061:
8058:
8056:
8053:
8051:
8048:
8046:
8043:
8041:
8038:
8036:
8033:
8031:
8028:
8026:
8023:
8021:
8018:
8017:
8015:
8011:
8008:
8004:
7998:
7995:
7993:
7990:
7988:
7985:
7983:
7980:
7978:
7977:String theory
7975:
7973:
7970:
7968:
7965:
7963:
7960:
7958:
7955:
7953:
7950:
7948:
7947:Axiomatic QFT
7945:
7943:
7942:Algebraic QFT
7940:
7939:
7937:
7933:
7929:
7922:
7917:
7915:
7910:
7908:
7903:
7902:
7899:
7885:on 2009-01-16
7884:
7880:
7876:
7872:
7862:on 2021-06-03
7861:
7857:
7853:
7849:
7845:
7841:
7840:
7835:
7831:
7830:
7826:
7813:
7809:
7805:
7800:
7795:
7790:
7789:
7785:
7784:
7779:
7777:981-238-934-2
7773:
7769:
7766:. Singapore:
7765:
7761:
7757:
7753:
7751:0-19-851961-3
7747:
7743:
7739:
7734:
7730:
7724:
7720:
7716:
7712:
7708:
7707:
7703:
7702:
7697:
7687:
7682:
7678:
7674:
7670:
7666:
7662:
7658:
7654:
7650:
7646:
7640:
7637:
7632:
7628:
7624:
7620:
7616:
7612:
7607:
7602:
7599:(7): 074034.
7598:
7594:
7593:
7578:
7575:
7570:
7566:
7562:
7558:
7554:
7550:
7546:
7542:
7537:
7532:
7528:
7524:
7523:
7515:
7512:
7507:
7501:
7497:
7490:
7487:
7482:
7478:
7471:
7468:
7463:
7459:
7455:
7451:
7445:
7443:
7439:
7433:
7432:gr-qc/0012054
7428:
7421:
7419:
7417:
7413:
7407:
7402:
7398:
7394:
7390:
7386:
7385:
7380:
7376:
7372:
7366:
7363:
7358:
7356:9781461301950
7352:
7348:
7347:
7344:
7336:
7333:
7328:
7322:
7318:
7311:
7309:
7307:
7305:
7303:
7299:
7294:
7290:
7286:
7282:
7278:
7274:
7270:
7263:
7261:
7257:
7246:
7242:
7236:
7233:
7226:
7221:
7218:
7216:
7213:
7211:
7208:
7206:
7203:
7201:
7198:
7196:
7193:
7191:
7188:
7186:
7183:
7181:
7178:
7176:
7170:
7168:
7165:
7163:
7160:
7158:
7155:
7153:
7150:
7148:
7145:
7143:
7140:
7138:
7135:
7133:
7132:Coulomb gauge
7130:
7128:
7125:
7124:
7119:
7117:
7115:
7110:
7108:
7103:
7099:
7095:
7091:
7086:
7084:
7080:
7076:
7069:Open problems
7068:
7066:
7060:
7056:
7052:
7048:
7044:
7040:
7035:
7033:
7029:
7022:
7018:
7013:
6993:
6990:
6987:
6983:
6959:
6951:
6947:
6938:
6935:
6931:
6925:
6912:
6909:
6906:
6902:
6893:
6883:
6867:
6865:
6861:
6853:
6845:
6818:
6811:
6803:
6798:
6794:
6784:
6781:
6778:
6770:
6767:
6764:
6761:
6757:
6747:
6739:
6734:
6730:
6723:
6718:
6705:
6700:
6690:
6684:
6681:
6674:
6670:
6667:
6663:
6656:
6648:
6644:
6634:
6631:
6628:
6620:
6617:
6613:
6603:
6595:
6585:
6575:
6570:
6557:
6552:
6542:
6539:
6535:
6531:
6528:
6525:
6519:
6516:
6507:
6501:
6498:
6490:
6486:
6478:
6477:
6476:
6452:
6449:
6440:
6434:
6431:
6423:
6419:
6415:
6410:
6401:
6391:
6383:
6380:
6376:
6369:
6364:
6358:
6346:
6338:
6335:
6331:
6324:
6319:
6316:
6298:
6290:
6285:
6281:
6274:
6269:
6263:
6248:
6240:
6235:
6231:
6224:
6219:
6213:
6205:
6202:
6199:
6195:
6186:
6183:
6180:
6176:
6169:
6164:
6154:
6149:
6144:
6140:
6131:
6128:
6124:
6120:
6117:
6114:
6110:
6101:
6091:
6083:
6080:
6076:
6069:
6064:
6058:
6043:
6035:
6030:
6026:
6019:
6014:
6008:
5996:
5988:
5983:
5979:
5972:
5967:
5961:
5953:
5943:
5940:
5937:
5933:
5926:
5921:
5911:
5908:
5902:
5899:
5895:
5891:
5888:
5885:
5882:
5873:
5863:
5855:
5851:
5844:
5839:
5833:
5818:
5810:
5805:
5801:
5794:
5789:
5783:
5772:
5762:
5759:
5756:
5752:
5739:
5731:
5721:
5711:
5705:
5701:
5693:
5688:
5678:
5675:
5669:
5666:
5662:
5658:
5655:
5652:
5650:
5642:
5639:
5630:
5624:
5621:
5615:
5604:
5603:
5602:
5596:
5592:
5582:
5559:
5553:
5549:
5540:
5537:
5533:
5524:
5511:
5508:
5505:
5501:
5492:
5482:
5472:
5469:
5464:
5460:
5454:
5444:
5431:
5421:
5413:
5406:
5401:
5391:
5388:
5385:
5380:
5376:
5365:
5364:
5363:
5341:
5333:
5330:
5318:
5313:
5303:
5297:
5294:
5290:
5285:
5282:
5277:
5274:
5270:
5262:
5261:
5260:
5239:
5233:
5230:
5226:
5217:
5214:
5210:
5205:
5201:
5198:
5192:
5187:
5177:
5171:
5168:
5162:
5159:
5154:
5150:
5142:
5141:
5140:
5118:
5113:
5106:
5098:
5094:
5084:
5076:
5066:
5059:
5053:
5045:
5041:
5031:
5023:
5013:
5005:
4998:
4993:
4983:
4980:
4977:
4971:
4963:
4960:
4956:
4949:
4941:
4936:
4932:
4925:
4920:
4910:
4907:
4903:
4899:
4896:
4880:
4876:
4873:
4864:
4858:
4855:
4852:
4843:
4834:
4831:
4824:
4818:
4814:
4807:
4804:
4800:
4796:
4789:
4783:
4780:
4776:
4769:
4766:
4762:
4758:
4755:
4752:
4745:
4736:
4732:
4725:
4715:
4712:
4703:
4680:
4660:
4646:
4643:
4641:
4633:
4630:
4621:
4615:
4612:
4606:
4595:
4594:
4593:
4591:
4587:
4583:
4579:
4575:
4571:
4567:
4566:gauge freedom
4548:
4541:
4534:
4526:
4523:
4519:
4509:
4501:
4496:
4492:
4485:
4480:
4470:
4464:
4461:
4457:
4451:
4448:
4444:
4435:
4432:
4428:
4423:
4419:
4416:
4410:
4405:
4395:
4389:
4386:
4380:
4376:
4372:
4369:
4360:
4349:
4346:
4340:
4334:
4324:
4323:
4322:
4316:
4308:
4306:
4304:
4300:
4292:
4286:
4270:
4263:
4257:
4253:
4250:
4247:
4243:
4238:
4234:
4230:
4226:
4221:
4217:
4213:
4185:
4179:
4173:
4169:
4166:
4163:
4156:
4151:
4147:
4143:
4139:
4136:
4133:
4116:
4099:
4091:
4086:
4082:
4078:
4075:
4070:
4065:
4062:
4058:
4049:
4046:
4042:
4033:
4030:
4027:
4023:
4016:
4013:
4008:
4003:
4000:
3996:
3990:
3975:
3974:
3973:
3954:
3949:
3945:
3918:
3912:
3909:
3904:
3901:
3891:
3882:
3878:
3867:
3866:
3865:
3851:
3843:
3840:
3836:
3830:
3827:
3824:
3821:
3817:
3810:
3807:
3801:
3796:
3793:
3783:
3768:
3752:
3744:
3739:
3736:
3732:
3723:
3719:
3715:
3711:
3705:
3700:
3697:
3693:
3689:
3684:
3680:
3675:
3645:
3642:
3638:
3633:
3627:
3623:
3619:
3614:
3610:
3605:
3601:
3596:
3592:
3587:
3583:
3579:
3574:
3568:
3564:
3560:
3555:
3551:
3546:
3542:
3537:
3533:
3528:
3524:
3520:
3515:
3509:
3505:
3501:
3496:
3492:
3487:
3483:
3478:
3474:
3469:
3458:
3457:
3456:
3455:
3433:
3430:
3425:
3420:
3414:
3411:
3407:
3398:
3394:
3389:
3384:
3379:
3374:
3368:
3365:
3361:
3352:
3348:
3343:
3338:
3333:
3328:
3322:
3319:
3315:
3306:
3302:
3297:
3285:
3284:
3283:
3281:
3262:
3256:
3253:
3248:
3243:
3237:
3234:
3230:
3224:
3220:
3215:
3203:
3202:
3201:
3187:
3179:
3174:
3171:
3167:
3161:
3157:
3153:
3148:
3145:
3141:
3114:
3108:
3105:
3100:
3095:
3092:
3088:
3079:
3076:
3072:
3063:
3060:
3057:
3053:
3046:
3043:
3038:
3033:
3030:
3026:
3020:
3005:
3004:
3003:
3000:
2987:
2978:
2975:
2972:
2969:
2947:
2942:
2939:
2935:
2906:
2903:
2900:
2896:
2892:
2887:
2884:
2881:
2877:
2865:
2860:
2858:
2838:
2830:
2825:
2822:
2818:
2809:
2805:
2798:
2792:
2789:
2786:
2782:
2776:
2772:
2768:
2763:
2759:
2754:
2743:
2742:
2741:
2740:
2716:
2711:
2707:
2698:
2693:
2689:
2680:
2677:
2674:
2670:
2663:
2660:
2655:
2650:
2646:
2640:
2632:
2627:
2622:
2618:
2612:
2604:
2599:
2594:
2591:
2587:
2576:
2575:
2574:
2573:The relation
2571:
2558:
2552:
2549:
2544:
2540:
2536:
2533:
2530:
2527:
2524:
2521:
2518:
2515:
2502:
2492:
2484:
2463:
2458:
2454:
2442:
2420:
2412:
2407:
2403:
2394:
2390:
2383:
2377:
2374:
2369:
2358:
2355:
2350:
2346:
2335:
2334:
2333:
2331:
2310:
2307:
2303:
2271:
2267:
2258:
2254:
2247:
2244:
2233:
2210:
2202:
2198:
2189:
2186:
2183:
2179:
2172:
2169:
2165:
2159:
2155:
2148:
2143:
2139:
2134:
2129:
2121:
2118:
2114:
2107:
2104:
2098:
2094:
2088:
2084:
2075:
2071:
2066:
2062:
2059:
2049:
2048:
2047:
2045:
2034:, indexed by
2033:
2012:
2008:
1976:
1971:
1968:
1964:
1958:
1955:
1952:
1948:
1941:
1938:
1932:
1929:
1921:
1917:
1910:
1907:
1901:
1898:
1892:
1889:
1860:
1859:
1858:
1857:
1843:
1839:
1830:
1826:
1816:
1808:
1804:
1800:
1786:
1782:
1776:
1773:is the third
1768:
1757:
1753:
1747:
1739:
1735:
1723:
1714:
1703:
1694:
1684:
1676:
1674:
1671:
1667:
1663:
1658:
1655:
1651:
1647:
1643:
1642:Kaluza, Klein
1639:
1635:
1631:
1623:
1621:
1619:
1616:problem is a
1615:
1611:
1607:
1606:Phenomenology
1603:
1601:
1593:
1589:
1585:
1582:combines the
1581:
1573:
1509:
1505:
1496:
1487:
1483:
1479:
1475:
1471:
1467:
1462:
1458:
1444:
1434:
1430:
1425:
1421:
1415:
1413:
1407:
1405:
1401:
1392:
1390:
1388:
1369:
1363:
1355:
1337:
1334:
1330:
1306:
1300:
1292:
1288:
1286:
1282:
1278:
1274:
1270:
1262:
1257:
1255:
1253:
1245:
1241:
1238:) as well as
1233:
1229:
1225:
1222:
1218:
1212:
1207:
1203:
1199:
1195:
1191:
1180:
1175:
1173:
1168:
1166:
1161:
1160:
1158:
1157:
1151:
1146:
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1121:
1120:Zamolodchikov
1118:
1116:
1115:Zamolodchikov
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1096:
1093:
1091:
1088:
1086:
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
996:
993:
991:
988:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
956:
953:
951:
948:
946:
943:
941:
938:
936:
933:
931:
928:
926:
923:
921:
918:
916:
913:
911:
908:
906:
903:
901:
898:
896:
893:
891:
888:
886:
883:
881:
878:
876:
873:
871:
868:
866:
863:
861:
858:
856:
853:
851:
848:
846:
843:
841:
838:
836:
833:
831:
828:
826:
823:
821:
818:
816:
813:
811:
808:
806:
803:
801:
798:
796:
793:
791:
788:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
601:
598:
596:
593:
591:
588:
586:
583:
581:
578:
576:
573:
571:
568:
566:
563:
561:
558:
556:
553:
551:
548:
546:
543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
516:
513:
511:
508:
506:
503:
501:
498:
496:
493:
491:
488:
486:
483:
481:
478:
476:
473:
471:
468:
466:
463:
461:
458:
456:
453:
451:
448:
447:
440:
439:
432:
429:
427:
424:
422:
419:
417:
416:Supersymmetry
414:
412:
411:String theory
409:
408:
402:
401:
394:
391:
389:
386:
384:
381:
379:
376:
375:
372:
367:
366:
359:
356:
354:
351:
349:
346:
344:
341:
339:
336:
334:
331:
329:
326:
325:
319:
318:
311:
308:
306:
303:
301:
298:
296:
293:
291:
288:
286:
283:
281:
278:
276:
273:
271:
268:
266:
263:
261:
258:
256:
253:
251:
248:
246:
243:
241:
238:
236:
233:
231:
228:
226:
223:
221:
218:
216:
213:
212:
206:
205:
198:
195:
193:
190:
188:
185:
183:
180:
178:
175:
173:
170:
168:
165:
163:
160:
158:
155:
153:
150:
148:
145:
144:
141:
136:
135:
128:
125:
123:
120:
118:
115:
113:
110:
108:
105:
103:
100:
98:
95:
93:
90:
88:
85:
84:
78:
77:
74:
71:
70:
66:
61:
57:
56:
53:
49:
44:
30:
19:
8483:
8412:Quantum foam
8352:Stueckelberg
8306:Chern–Simons
8243:Supergravity
8074:
7982:Supergravity
7967:Gauge theory
7887:. Retrieved
7883:the original
7864:. Retrieved
7860:the original
7855:
7837:
7815:. Retrieved
7763:
7737:
7714:
7711:Frampton, P.
7660:
7656:
7639:
7596:
7590:
7577:
7526:
7520:
7514:
7495:
7489:
7476:
7470:
7461:
7460:(memorial).
7457:
7388:
7382:
7365:
7346:
7342:
7335:
7316:
7276:
7272:
7248:. Retrieved
7244:
7235:
7167:Lorenz gauge
7111:
7096:'s list of "
7087:
7072:
7039:a posteriori
7036:
7014:
6868:
6837:
6474:
5600:
5578:
5361:
5258:
5138:
4577:
4574:Victor Popov
4563:
4312:
4309:Quantization
4290:
4117:
4114:
3933:
3663:
3451:
3277:
3129:
3001:
2863:
2861:
2853:
2736:
2572:
2500:
2435:
2225:
1996:
1853:
1828:
1814:
1806:
1802:
1798:
1784:
1780:
1775:Pauli matrix
1766:
1755:
1751:
1737:
1733:
1659:
1627:
1604:
1500:SU(2) × U(1)
1490:SU(2) × U(1)
1463:
1460:
1436:
1417:
1409:
1404:Robert Mills
1396:
1289:
1277:group theory
1273:Emmy Noether
1269:Hermann Weyl
1266:
1244:strong force
1236:U(1) × SU(2)
1210:
1202:gauge theory
1198:Robert Mills
1189:
1188:
1149:
995:Stueckelberg
725:Jona-Lasinio
300:Vacuum state
285:Quantization
126:
122:Gauge theory
102:Strong force
87:Field theory
29:
8294:Topological
8208:Wess–Zumino
8121:Sine-Gordon
8111:Gross–Neveu
8020:Born–Infeld
7987:Thermal QFT
7649:Veltman, M.
7279:(1): 1–23.
7107:confinement
6864:decay rates
4578:ghost field
3765:Define the
2032:Lie algebra
1670:Abdus Salam
1654:gauge field
1610:confinement
1506:to produce
1232:weak forces
1221:non-abelian
1204:based on a
1135:Zinn-Justin
985:Sommerfield
910:Pomeranchuk
875:Osterwalder
870:Oppenheimer
800:Łopuszański
620:Fredenhagen
421:Technicolor
8505:Categories
8075:Yang–Mills
7889:2008-11-24
7866:2018-08-30
7817:2015-05-05
7464:: 137–146.
7450:Atiyah, M.
7371:Yang, C.N.
7250:2024-04-09
7227:References
7205:Weyl gauge
7180:Propagator
2739:commutator
2226:Here, the
1856:Lagrangian
1760:-slice of
1681:See also:
1650:Lagrangian
1502:mix after
1246:(based on
1224:Lie groups
1130:Zimmermann
1025:Vainshtein
900:Polchinski
760:Kontsevich
705:Iliopoulos
680:Heisenberg
505:Bogoliubov
443:Scientists
280:Propagator
162:T-symmetry
157:P-symmetry
152:C-symmetry
140:Symmetries
97:Weak force
81:Background
18:Yang-Mills
8484:See also:
8203:Super QCD
8157:Liouville
8145:Conformal
8116:Schwinger
7844:EMS Press
7808:Gross, D.
7719:Wiley-VCH
7686:1874/4845
7631:119434312
7375:Mills, R.
7293:0034-6861
6939:μ
6926:μ
6922:∂
6887:¯
6799:ν
6782:−
6771:ν
6768:μ
6735:μ
6691:∫
6671:
6645:ε
6632:−
6589:¯
6586:ε
6543:∫
6540:−
6532:
6520:ε
6511:¯
6508:ε
6453:ε
6444:¯
6441:ε
6416:×
6384:ν
6370:δ
6365:δ
6339:μ
6325:δ
6320:δ
6286:ν
6275:δ
6270:δ
6236:μ
6225:δ
6220:δ
6155:∫
6129:−
6121:
6115:×
6084:ν
6070:δ
6065:δ
6031:μ
6020:δ
6015:δ
5984:ν
5973:δ
5968:δ
5954:μ
5950:∂
5912:∫
5900:−
5892:
5886:×
5852:ε
5845:δ
5840:δ
5806:μ
5795:δ
5790:δ
5773:μ
5769:∂
5725:¯
5722:ε
5712:δ
5702:δ
5679:∫
5667:−
5659:
5643:ε
5634:¯
5631:ε
5541:μ
5525:μ
5521:∂
5486:¯
5455:μ
5451:∂
5445:μ
5441:∂
5425:¯
5392:∫
5389:−
5331:⋅
5328:∂
5304:∫
5298:ξ
5286:−
5234:ν
5231:μ
5218:ν
5215:μ
5202:
5178:∫
5163:−
5070:¯
5067:ε
5042:ε
5017:¯
4984:∫
4964:μ
4937:μ
4911:∫
4900:
4868:¯
4847:¯
4838:∂
4829:∂
4794:∂
4750:∂
4716:
4684:¯
4647:∫
4634:ε
4625:¯
4622:ε
4527:μ
4497:μ
4471:∫
4452:ν
4449:μ
4436:ν
4433:μ
4420:
4396:∫
4381:−
4373:
4350:∫
4251:−
4167:−
4087:ν
4079:−
4066:ν
4063:μ
4050:μ
4004:ν
4001:μ
3991:μ
3987:∂
3950:μ
3934:A source
3905:ν
3902:μ
3895:~
3883:μ
3844:σ
3841:ρ
3831:σ
3828:ρ
3825:ν
3822:μ
3818:ε
3797:ν
3794:μ
3787:~
3740:κ
3737:ν
3724:μ
3701:κ
3698:ν
3685:μ
3628:μ
3615:κ
3597:ν
3569:ν
3556:μ
3538:κ
3510:κ
3497:ν
3479:μ
3415:μ
3412:κ
3399:ν
3369:ν
3366:μ
3353:κ
3323:κ
3320:ν
3307:μ
3238:ν
3235:μ
3225:μ
3175:ν
3172:μ
3149:ν
3146:μ
3096:ν
3093:μ
3077:μ
3034:ν
3031:μ
3021:μ
3017:∂
2979:−
2976:−
2973:−
2943:ν
2940:μ
2936:η
2826:ν
2823:μ
2790:−
2777:ν
2764:μ
2712:ν
2694:μ
2651:μ
2641:ν
2637:∂
2633:−
2623:ν
2613:μ
2609:∂
2595:ν
2592:μ
2550:−
2537:…
2459:μ
2408:μ
2375:−
2370:μ
2366:∂
2351:μ
2304:δ
2248:
2115:δ
2063:
2044:curvature
1972:ν
1969:μ
1959:ν
1956:μ
1933:−
1911:
1893:−
1838:instanton
1338:θ
1065:Wetterich
1050:Weisskopf
1000:Sudarshan
950:Schwinger
860:Nishijima
825:Maldacena
790:Leutwyler
750:Kinoshita
650:Goldstone
640:Gell-Mann
555:Doplicher
322:Equations
8516:Symmetry
8280:Type IIB
8275:Type IIA
8260:4D N = 8
8255:4D N = 1
8224:6D (2,0)
8188:4D N = 1
8167:Polyakov
8126:Thirring
7935:Theories
7810:(1992).
7786:Articles
7713:(2008).
7651:(1972).
7569:42504317
7561:16711979
7452:(2017).
7377:(1954).
7120:See also
7100:". Here
7055:glueball
3130:Putting
2228:f
1080:Wightman
1045:Weinberg
1035:Virasoro
1015:Tomonaga
1010:Thirring
1005:Symanzik
965:Semenoff
940:Schrader
905:Polyakov
820:Majorana
755:Klebanov
710:Ivanenko
700:'t Hooft
670:Guralnik
615:Fröhlich
610:Fritzsch
605:Frampton
520:Buchholz
465:Bargmann
455:Anderson
235:Crossing
8382:History
8365:Related
8162:Minimal
8013:Regular
7846:, 2001
7665:Bibcode
7611:Bibcode
7541:Bibcode
7393:Bibcode
7059:hybrids
7047:hadrons
7041:in the
2489:is the
2481:is the
2439:is the
2328:), the
2030:of the
1823:on the
1748:on the
1422:, e.g.
1400:isospin
1090:Wilczek
1055:Wentzel
1030:Veltman
975:Shirkov
970:Shifman
960:Seiberg
945:Schwarz
925:Rubakov
845:Naimark
795:Lipatov
785:Lehmann
765:Kreimer
745:Kendall
635:Gelfand
630:Glashow
590:Feynman
570:Faddeev
565:Englert
535:Coleman
525:Cachazo
510:Brodsky
495:Bjorken
485:Berezin
475:Belavin
215:Anomaly
73:History
8322:Chiral
8270:Type I
8085:Yukawa
8006:Models
7877:. The
7774:
7748:
7725:
7629:
7567:
7559:
7502:
7353:
7323:
7291:
6999:
6980:
6957:
6944:
6918:
6899:
6877:
6823:
6791:
6754:
6727:
6709:
6641:
6610:
6579:
6561:
6373:
6362:
6328:
6314:
6308:
6278:
6267:
6258:
6228:
6217:
6192:
6173:
6135:
6073:
6062:
6053:
6023:
6012:
5976:
5965:
5930:
5906:
5848:
5837:
5828:
5798:
5787:
5778:
5749:
5715:
5709:
5697:
5673:
5564:
5546:
5530:
5517:
5498:
5476:
5437:
5410:
5373:
5347:
5322:
5244:
5223:
5196:
5139:being
5091:
5038:
5002:
4929:
4811:
4773:
4742:
4729:
4710:
4701:
4675:
4658:
4546:
4516:
4489:
4468:
4441:
4414:
4367:
4332:
4268:
4210:
4190:
4130:
4097:
4055:
4039:
4020:
3983:
3960:
3942:
3916:
3875:
3849:
3777:
3750:
3729:
3672:
3664:since
3649:
3466:
3437:
3404:
3358:
3312:
3293:
3282:holds
3260:
3211:
3185:
3138:
3112:
3085:
3069:
3050:
3013:
2985:
2932:
2912:
2874:
2836:
2815:
2802:
2796:
2751:
2722:
2704:
2686:
2667:
2584:
2556:
2513:
2483:vector
2469:
2451:
2418:
2400:
2387:
2381:
2362:
2343:
2316:
2300:
2280:
2264:
2242:
2208:
2195:
2176:
2152:
2127:
2081:
2057:
2018:
2005:
1982:
1868:
1764:where
1572:photon
1550:, and
1476:, and
1234:(i.e.
1145:Zumino
1110:Yukawa
1100:Witten
1095:Wilson
1085:Wigner
1020:Tyutin
980:Skyrme
930:Ruelle
895:Plefka
890:Peskin
880:Parisi
840:Møller
830:Migdal
815:Maiani
810:Lüders
775:Landau
770:Kuraev
740:Källén
730:Jordan
715:Jackiw
655:Gribov
545:DeWitt
540:Dashen
530:Callan
500:Bleuer
470:Becchi
460:Anselm
8461:links
8434:links
8422:links
8342:NMSSM
8327:Fermi
8070:Soler
8040:Proca
7794:arXiv
7704:Books
7627:S2CID
7601:arXiv
7565:S2CID
7531:arXiv
7427:arXiv
6475:with
4580:(see
1795:with
1652:of a
1495:SU(3)
1429:SU(2)
1248:SU(3)
1140:Zuber
990:Stora
955:Segal
935:Salam
920:Proca
915:Popov
885:Pauli
865:Oehme
855:Neveu
850:Nambu
835:Mills
720:Jaffe
695:Hagen
690:Higgs
665:Gupta
660:Gross
645:Glimm
625:Furry
595:Fierz
585:Fermi
580:Fayet
575:Fadin
560:Dyson
550:Dirac
515:Brout
490:Bethe
450:Adler
209:Tools
8332:MSSM
8229:ABJM
8136:Toda
7772:ISBN
7746:ISBN
7723:ISBN
7557:PMID
7500:ISBN
7462:2017
7351:ISBN
7321:ISBN
7289:ISSN
7057:and
6862:and
4572:and
3767:dual
2230:are
1805:=1,
1801:=2,
1730:The
1646:Fock
1590:and
1588:weak
1576:U(1)
1484:and
1230:and
1196:and
1105:Yang
1075:Wick
1070:Weyl
1060:Wess
1040:Ward
735:Jost
685:Hepp
675:Haag
600:Fock
480:Bell
8285:11D
7681:hdl
7673:doi
7619:doi
7549:doi
7401:doi
7281:doi
6668:exp
6529:exp
6118:exp
5889:exp
5656:exp
4897:exp
4713:exp
4370:exp
4293:= 4
2499:SU(
1844:on
1832:of
1636:of
1209:SU(
1125:Zee
805:Low
780:Lee
8507::
8301:BF
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7836:,
7770:.
7744:.
7740:.
7721:.
7679:.
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7625:.
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7597:76
7595:.
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7415:^
7399:.
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7301:^
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7259:^
7243:.
7116:.
7085:.
7034:.
5199:tr
4417:tr
3278:A
2245:tr
2060:tr
1908:tr
1817:=0
1809:=0
1644:,
1620:.
1530:,
1472:,
1287:.
7920:e
7913:t
7906:v
7892:.
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7435:.
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7403::
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7063:σ
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6994:c
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6948:c
6936:b
6932:A
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6812:y
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6682:1
6675:(
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6626:(
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6389:(
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6264:i
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6246:(
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6141:g
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6125:(
6102:)
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5694:x
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5684:d
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5670:i
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5640:,
5625:,
5622:j
5619:[
5616:Z
5589:ξ
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5560:)
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5550:c
5538:b
5534:A
5512:c
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5502:f
5493:a
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5470:+
5465:a
5461:c
5432:a
5422:c
5414:(
5407:x
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5325:(
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5211:F
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5119:}
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5110:)
5107:x
5104:(
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4805:+
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4759:A
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4753:A
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4721:{
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4704:c
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4693:[
4690:]
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4214:[
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4076:=
4071:c
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2036:a
2013:a
2009:T
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1939:1
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1922:2
1918:F
1914:(
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1846:ℝ
1834:ℝ
1829:S
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