4031:. The parity is odd for orbitals p, f, ... with ℓ = 1, 3, ..., and an atomic state has odd parity if an odd number of electrons occupy these orbitals. For example, the ground state of the nitrogen atom has the electron configuration 1s2s2p, and is identified by the term symbol S, where the superscript o denotes odd parity. However the third excited term at about 83,300 cm above the ground state has electron configuration 1s2s2p3s has even parity since there are only two 2p electrons, and its term symbol is P (without an o superscript).
5262:
5276:
5382:. As the experiment was winding down, with double-checking in progress, Wu informed Lee and Yang of their positive results, and saying the results need further examination, she asked them not to publicize the results first. However, Lee revealed the results to his Columbia colleagues on 4 January 1957 at a "Friday lunch" gathering of the Physics Department of Columbia. Three of them,
502:-reflections) one can recover the particular parity transformation defined earlier. The first parity transformation given does not work in an even number of dimensions, though, because it results in a positive determinant. In even dimensions only the latter example of a parity transformation (or any reflection of an odd number of coordinates) can be used.
1190:
2999:, one can always take linear combinations of quantum states such that they are either even or odd under parity (see the figure). Thus the parity of such states is ±1. The parity of a multiparticle state is the product of the parities of each state; in other words parity is a multiplicative quantum number.
293:
refers to the fact that if one projects out the phase of each state, where we recall that the overall phase of a quantum state is not observable, then a projective representation reduces to an ordinary representation. All representations are also projective representations, but the converse is not
5124:
Since the orbital momentum changes from zero to one in this process, if the process is to conserve the total parity then the products of the intrinsic parities of the initial and final particles must have opposite sign. A deuteron nucleus is made from a proton and a neutron, and so using the
4324:
is used; the vacuum state is then invariant under parity by construction. The invariance of the action follows from the classical invariance of
Maxwell's equations. The invariance of the canonical quantization procedure can be worked out, and turns out to depend on the transformation of the
3481:
5339:
By the mid-20th century, it had been suggested by several scientists that parity might not be conserved (in different contexts), but without solid evidence these suggestions were not considered important. Then, in 1956, a careful review and analysis by theoretical physicists
1067:
709:. These are useful in quantum mechanics. However, as is elaborated below, in quantum mechanics states need not transform under actual representations of parity but only under projective representations and so in principle a parity transformation may rotate a state by any
4015:
The overall parity of a many-particle system is the product of the parities of the one-particle states. It is −1 if an odd number of particles are in odd-parity states, and +1 otherwise. Different notations are in use to denote the parity of nuclei, atoms, and molecules.
2102:
Two dimensional representations of parity are given by a pair of quantum states which go into each other under parity. However, this representation can always be reduced to linear combinations of states, each of which is either even or odd under parity. One says that all
4006:
5390:, and R. M. Weinrich, modified an existing cyclotron experiment, and immediately verified the parity violation. They delayed publication of their results until after Wu's group was ready, and the two papers appeared back-to-back in the same physics journal.
164:
486:
5040:, which implies that the final state is antisymmetric. Using the fact that the deuteron has spin one and the pion spin zero together with the antisymmetry of the final state they concluded that the two neutrons must have orbital angular momentum
4176:. As for electrons in atoms, the nucleon state has odd overall parity if and only if the number of nucleons in odd-parity states is odd. The parity is usually written as a + (even) or − (odd) following the nuclear spin value. For example, the
5312:
gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in charged weak interactions in the
Standard Model. This implies that parity is not a symmetry of our universe, unless a
2265:
4405:
2355:
2099:
4549:
4619:
2606:
2943:
The law of conservation of parity of particles states that, if an isolated ensemble of particles has a definite parity, then the parity remains invariable in the process of ensemble evolution. However this is not true for the
4251:
3865:
4180:
include O(5/2+), meaning that the spin is 5/2 and the parity is even. The shell model explains this because the first 16 nucleons are paired so that each pair has spin zero and even parity, and the last nucleon is in the
2940:(potential energy invariant with respect to a space inversion, symmetric to the origin), either remain invariable or change signs: these two possible states are called the even state or odd state of the wave functions.
4097:
commutes with the rovibronic (rotation-vibration-electronic) Hamiltonian and can be used to label such states. Electronic and vibrational states of centrosymmetric molecules are either unchanged by the operation
721:
An alternative way to write the above classification of scalars, pseudoscalars, vectors and pseudovectors is in terms of the representation space that each object transforms in. This can be given in terms of the
3351:
3927:
4039:
The complete (rotational-vibrational-electronic-nuclear spin) electromagnetic
Hamiltonian of any molecule commutes with (or is invariant to) the parity operation P (or E*, in the notation introduced by
3198:
1319:
The answers given below are correct for 3 spatial dimensions. In a 2 dimensional space, for example, when constrained to remain on the surface of a planet, some of the variables switch sides.
202:
By contrast, in interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.
63:
3290:
588:
2724:
1072:
1300:
The two major divisions of classical physical variables have either even or odd parity. The way into which particular variables and vectors sort out into either category depends on whether the
707:
664:
386:
5236:
5003:
1185:{\displaystyle {\begin{aligned}\mathbf {L} &=\mathbf {r} \times \mathbf {p} \\{\hat {P}}\left(\mathbf {L} \right)&=(-\mathbf {r} )\times (-\mathbf {p} )=\mathbf {L} .\end{aligned}}}
2760:
2642:
1033:
2461:
2393:
4328:
5122:
3922:
3803:
3739:
3708:
3039:
2673:
2144:
3081:
1518:
1035:(if the mass is constant) equates two vectors, and hence is invariant under parity. The law of gravity also involves only vectors and is also, therefore, invariant under parity.
783:
195:, the weak interaction is chiral and thus provides a means for probing chirality in physics. In her experiment, Wu took advantage of the controlling role of weak interactions in
958:
5612:
Mladen
Georgiev (20 November 2008). "Parity non-conservation in β-decay of nuclei: revisiting experiment and theory fifty years after. IV. Parity breaking models". p. 26.
5154:
they argued that the parity of the pion is equal to minus the product of the parities of the two neutrons divided by that of the proton and neutron in the deuteron, explicitly
3113:
2997:
868:
621:
535:
4554:
3141:
992:
4427:
2931:
2901:
2031:
2004:
1976:
1940:
1705:
1678:
1651:
1624:
1597:
1570:
1542:
1486:
1458:
1430:
1402:
1282:
1260:
1238:
1058:
5853:
5809:
3772:
3677:
3648:
3619:
3550:
3319:
3227:
2423:
2173:
905:
821:
5919:
2835:
corresponds to odd functions. However, when no such symmetry group exists, it may be that all parity transformations have some eigenvalues which are phases other than
2524:
2273:
5739:
5073:
3808:
2491:
2066:
4307:
3346:
2856:
2783:
2168:
1909:
1851:
1375:
1216:
743:
5765:
5152:
4447:
4056:
as they are even or odd, respectively. The parity operation involves the inversion of electronic and nuclear spatial coordinates at the molecular center of mass.
5431:
To every particle one can assign an intrinsic parity as long as nature preserves parity. Although weak interactions do not, one can still assign a parity to any
4467:
2833:
2806:
5027:
3887:
1876:
1821:
1795:
1769:
1743:
1350:
4091:
involves the inversion of the electronic and vibrational displacement coordinates at the nuclear centre of mass. For centrosymmetric molecules the operation
2529:
4200:
2395:, which reverses the parity of a state twice, leaves the spacetime invariant, and so is an internal symmetry which rotates its eigenstates by phases
5715:
Pique, J. P.; et al. (1984). "Hyperfine-Induced
Ungerade-Gerade Symmetry Breaking in a Homonuclear Diatomic Molecule near a Dissociation Limit:
4320:
is invariant under parity, we have to prove that the action is invariant and the quantization is also invariant. For simplicity we will assume that
6377:
4887:
is no longer part of the continuous symmetry group and the desired redefinition of the parity operator cannot be performed. Instead it satisfies
4059:
Centrosymmetric molecules at equilibrium have a centre of symmetry at their midpoint (the nuclear center of mass). This includes all homonuclear
4172:
In atomic nuclei, the state of each nucleon (proton or neutron) has even or odd parity, and nucleon configurations can be predicted using the
6588:
6223:
5646:
5596:
5419:, suggested that parity may also be violated in the strong interaction. It is predicted that this local parity violation manifests itself by
490:
which also have negative determinant and form a valid parity transformation. Then, combining them with rotations (or successively performing
6665:
3476:{\displaystyle {\hat {\mathcal {P}}}{\bigl |}{\vec {L}},L_{z}{\bigr \rangle }=\left(-1\right)^{L}{\bigl |}{\vec {L}},L_{z}{\bigr \rangle }}
294:
true, therefore the projective representation condition on quantum states is weaker than the representation condition on classical states.
5356:. They proposed several possible direct experimental tests. They were mostly ignored, but Lee was able to convince his Columbia colleague
6361:
5075:
The total parity is the product of the intrinsic parities of the particles and the extrinsic parity of the spherical harmonic function
2959:, and the particle state is defined by three quantum numbers: total energy, angular momentum and the projection of angular momentum.
6634:
6611:
6565:
6407:"Observations of the failure of conservation of parity and charge conjugation in meson decays: The magnetic moment of the free muon"
6386:
6007:
5979:
5564:
5539:
5501:
An example of a mass flow rate would the direction and rate, by weight, at which a river moves sediment. It is a composite form of
4134:
The complete electromagnetic
Hamiltonian of a centrosymmetric molecule does not commute with the point group inversion operation
3146:
5408:
5332:
explored, without any evidence, the existence of a two-component massless particle of spin one-half. This idea was rejected by
4140:
because of the effect of the nuclear hyperfine
Hamiltonian. The nuclear hyperfine Hamiltonian can mix the rotational levels of
3239:
3003:
6448:
Kharzeev, D.E.; Liao, J. (2 January 2019). "Isobar collisions at RHIC to test local parity violation in strong interactions".
5435:
by examining the strong interaction reaction that produces it, or through decays not involving the weak interaction, such as
242:
6770:
540:
6760:
5365:
188:
669:
626:
6499:
Zhao, Jie; Wang, Fuqiang (July 2019). "Experimental searches for the chiral magnetic effect in heavy-ion collisions".
5349:
4972:
4464:
A straightforward extension of these arguments to scalar field theories shows that scalars have even parity. That is,
4041:
1627:
1353:
591:
5157:
5037:
4001:{\displaystyle {\hat {\mathcal {P}}}^{2}\left|\psi \right\rangle =c\,{\hat {\mathcal {P}}}\left|\psi \right\rangle .}
2678:
218:, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is
6780:
6765:
6626:
6603:
2104:
159:{\displaystyle \mathbf {P} :{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto {\begin{pmatrix}-x\\-y\\-z\end{pmatrix}}.}
4671:
must act as one of the internal symmetries of the theory, at most changing the phase of a state. For example, the
54:. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a
2956:
286:
6356:] (in Chinese). 江才健 (author/biographer). 時報文化出版企業股份有限公司 (Times Culture Publishing Enterprise). p. 216.
1005:
6785:
6775:
6658:
4821:
4028:
2428:
2360:
1328:
Classical variables whose signs flip when inverted in space inversion are predominantly vectors. They include:
302:
2955:
The parity of the states of a particle moving in a spherically symmetric external field is determined by the
6580:
5584:
5078:
4317:
2729:
2611:
48:
5412:
3896:
3777:
3713:
3682:
3013:
2647:
2118:
5420:
4321:
3805:
and the others are merely reversed in sign when the
Hamiltonian operator and the parity operator commute:
3044:
with the
Hamiltonian. In non-relativistic quantum mechanics, this happens for any scalar potential, i.e.,
2809:
1721:
Classical variables, predominantly scalar quantities, which do not change upon spatial inversion include:
1285:
481:{\displaystyle V_{x}:{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto {\begin{pmatrix}-x\\y\\z\end{pmatrix}},}
332:
230:
5378:, Hayward, Hoppes, and Hudson (1957) found a clear violation of parity conservation in the beta decay of
3047:
1497:
748:
301:
of the group. For example, projective representations of the 3-dimensional rotation group, which is the
6073:
Chinowsky, W.; Steinberger, J. (1954). "Absorption of
Negative Pions in Deuterium: Parity of the Pion".
5328:, but, since the appropriate concepts had not yet been developed, those results had no impact. In 1929,
5267:
P-symmetry: A clock built like its mirrored image behaves like the mirrored image of the original clock.
5239:
2069:
1916:
1654:
913:
306:
3090:
2973:
829:
597:
511:
6518:
6457:
6420:
6317:
6267:
6120:
6084:
6039:
5930:
5864:
5687:
4076:
268:
4309:
and the quantization conditions remain unchanged under parity, then it follows that every state has
3118:
966:
316:
If one adds to this a classification by parity, these can be extended, for example, into notions of
229:
In quantum mechanics, wave functions that are unchanged by a parity transformation are described as
172:
of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image.
6729:
6651:
6167:
5664:
To read the nitrogen atom energy levels, type "N I" in the Spectrum box and click on Retrieve data.
5309:
4310:
4173:
4072:
3007:
2260:{\displaystyle {\hat {\mathcal {P}}}\,\psi {\left(r\right)}=e^{{i\phi }/{2}}\psi {\left(-r\right)}}
282:
176:
169:
5348:
went further, showing that while parity conservation had been verified in decays by the strong or
5261:
4410:
2906:
2876:
2014:
1987:
1959:
1923:
1688:
1661:
1634:
1607:
1580:
1553:
1525:
1469:
1441:
1413:
1385:
1265:
1243:
1221:
1041:
6790:
6739:
6534:
6508:
6481:
6371:
6184:
6055:
5814:
5770:
5613:
5472:
5462:
5416:
5301:
4458:
4400:{\displaystyle \mathbf {Pa} (\mathbf {p} ,\pm )\mathbf {P} ^{+}=\mathbf {a} (-\mathbf {p} ,\pm )}
4177:
1882:
1289:
723:
3748:
3653:
3624:
3558:
3489:
3295:
3203:
2398:
2350:{\displaystyle {\hat {\mathcal {P}}}^{2}\,\psi {\left(r\right)}=e^{i\phi }\psi {\left(r\right)}}
875:
791:
309:
SU(2). Projective representations of the rotation group that are not representations are called
297:
The projective representations of any group are isomorphic to the ordinary representations of a
5971:
5965:
5890:
Critchley, A. D. J.; et al. (2001). "Direct Measurement of a Pure Rotation Transition in H
6630:
6607:
6584:
6561:
6473:
6382:
6357:
6219:
6003:
5975:
5946:
5893:
5642:
5592:
5560:
5535:
5275:
4910:
4801:
4449:
refers to its polarization state. This is equivalent to the statement that the photon has odd
4060:
3230:
1405:
274:
264:
196:
4824:
counting how many fermions are in a state. Since all particles in the Standard Model satisfy
2496:
6526:
6465:
6428:
6325:
6275:
6211:
6176:
6092:
6047:
5938:
5872:
5718:
5695:
5353:
5293:
5043:
4967:
4914:
4859:
4450:
2949:
2466:
2147:
2041:
1943:
1879:
1681:
256:
252:
223:
180:
55:
6114:
5661:
4544:{\displaystyle {\mathsf {P}}\phi (-\mathbf {x} ,t){\mathsf {P}}^{-1}=\phi (\mathbf {x} ,t)}
4256:
3324:
2838:
2765:
2153:
1894:
1836:
1360:
1201:
728:
6411:
6308:
6295:
6258:
6075:
6027:
6023:
5995:
5744:
5502:
5371:
5357:
5128:
4698:
4432:
3083:, hence the potential is spherically symmetric. The following facts can be easily proven:
1824:
1708:
1573:
1545:
1489:
1195:
298:
192:
233:
functions, while those that change sign under a parity transformation are odd functions.
6522:
6461:
6424:
6321:
6271:
6204:"The Discovery of the Parity Violation in Weak Interactions and Its Recent Developments"
6088:
6043:
5934:
5868:
5691:
2815:
2788:
6398:
6249:
6203:
6110:
5383:
5345:
5333:
5012:
4672:
4626:
4614:{\displaystyle \mathbf {Pa} (\mathbf {p} )\mathbf {P} ^{+}=\mathbf {a} (-\mathbf {p} )}
4024:
3872:
2937:
2112:
2007:
1979:
1951:
1947:
1912:
1861:
1854:
1828:
1806:
1780:
1754:
1728:
1600:
1335:
3650:
is also an eigenstate of the parity operator; i.e., a non-degenerate eigenfunction of
6754:
6538:
6485:
6402:
6299:
6245:
6188:
6059:
5638:
5467:
5387:
5375:
5341:
5314:
5251:
5125:
aforementioned convention that protons and neutrons have intrinsic parities equal to
4689:
4680:
2968:
2861:
For electronic wavefunctions, even states are usually indicated by a subscript g for
2034:
1378:
710:
506:
278:
184:
17:
994:, scalars and pseudoscalars transform identically, as do vectors and pseudovectors.
6716:
6711:
5457:
5329:
5324:, G. C. McIlwraith, and B. Kurrelmeyer, had in effect reported parity violation in
4676:
4454:
4194:
2869:(German: odd). For example, the lowest energy level of the hydrogen molecule ion (H
1461:
1061:
362:
6469:
6210:, Lecture Notes in Physics, vol. 746, Tokyo: Springer Japan, pp. 43–70,
4663:
Applying the parity operator twice leaves the coordinates unchanged, meaning that
2601:{\displaystyle {\hat {\mathcal {P}}}'\equiv {\hat {\mathcal {P}}}\,e^{-{iQ}/{2}}}
6215:
5942:
4246:{\displaystyle {\hat {\mathcal {P}}}\left|0\right\rangle =\left|0\right\rangle }
211:
6530:
5876:
3860:{\displaystyle {\hat {\mathcal {P}}}|\psi \rangle =c\left|\psi \right\rangle ,}
6693:
6683:
5700:
5675:
5477:
5452:
5325:
4927:
4804:
then this element need not exist and such a redefinition may not be possible.
4641:
3890:
3552:, then atomic dipole transitions only occur between states of opposite parity.
3041:
2945:
2526:
is part of this U(1) and so is also a symmetry. In particular, we can define
2080:
2075:
All masses, charges, coupling constants, and other scalar physical constants,
51:
6477:
6433:
6406:
6330:
6303:
4658:
2936:
The wave functions of a particle moving into an external potential, which is
313:
and so quantum states may transform not only as tensors but also as spinors.
6734:
6280:
6253:
6138:
6096:
5436:
5379:
5361:
5321:
4734:
can always be constructed by multiplying it by an internal symmetry such as
6602:. Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology.
5950:
2098:
6706:
6643:
4922:
4862:
4064:
1433:
248:
215:
4079:. For centrosymmetric molecules, the point group contains the operation
6180:
6143:
6051:
5300:, it is violated in weak interactions, and perhaps, to some degree, in
5297:
5033:
5006:
4818:
4637:
4630:
4068:
623:, there are two irreducible representations: one is even under parity,
33:
5432:
4921:
has negative parity. They studied the decay of an "atom" made from a
4622:
4085:
which is not to be confused with the parity operation. The operation
1798:
310:
260:
4851:, then it can be redefined to give a new parity operator satisfying
6513:
6139:"For one tiny instant, physicists may have broken a law of nature"
5618:
5589:
Atomic spectroscopy. Introduction of theory to Hyperfine Structure
5506:
2097:
1296:
Effect of spatial inversion on some variables of classical physics
199:
of atomic isotopes to establish the chirality of the weak force.
4730:. This operator is also not unique in that a new parity operator
5440:
5401:
5394:
4918:
4640:, there is a slight complication because there is more than one
1886:
1772:
1746:
6647:
4756:
To see if the parity operator can always be defined to satisfy
6116:
The Ambidextrous Universe; Left, Right, and the Fall of Parity
2493:
of a continuous U(1) symmetry group of phase rotations, then
6002:. Vol. 4. Cambridge University Press. pp. 124–126.
5411:
had created a short-lived parity symmetry-breaking bubble in
5281:
P-asymmetry: A clock built like its mirrored image that does
4044:) and its eigenvalues can be given the parity symmetry label
5393:
The discovery of parity violation explained the outstanding
5364:
facilities and expertise, so the experiment was done at the
4844:
continuous symmetry group. If the parity operator satisfied
4777:
present in the theory. The desired parity operator would be
4284:
4208:
3974:
3936:
3904:
3816:
3785:
3721:
3690:
3588:
3519:
3359:
3021:
2738:
2689:
2655:
2620:
2559:
2538:
2437:
2369:
2282:
2181:
2126:
1304:
of space is either an odd or even number. The categories of
677:
634:
549:
4894:
so the Majorana neutrinos would have intrinsic parities of
3193:{\displaystyle \langle \varphi |{\hat {X}}|\psi \rangle =0}
5407:
In 2010, it was reported that physicists working with the
4621:
This is true even for a complex scalar field. (Details of
4185:
shell, which has even parity since ℓ = 2 for a d orbital.
4858:. But if the Standard Model is extended by incorporating
3285:{\displaystyle {\bigl |}{\vec {L}},L_{z}{\bigr \rangle }}
2608:, which is also a symmetry, and so we can choose to call
6304:"Experimental test of parity conservation in beta decay"
5317:
exists in which parity is violated in the opposite way.
5415:. An experiment conducted by several physicists in the
2903:
and the next-closest (higher) energy level is labelled
2357:, since an overall phase is unobservable. The operator
2111:
In quantum mechanics, spacetime transformations act on
251:, classical geometrical objects can be classified into
6254:"Question of Parity Conservation in Weak Interactions"
5160:
4313:
parity, and this parity is conserved in any reaction.
444:
408:
281:
do not need to transform under representations of the
116:
80:
5896:
5817:
5773:
5747:
5721:
5131:
5081:
5046:
5015:
4975:
4557:
4470:
4435:
4413:
4331:
4259:
4203:
3930:
3899:
3875:
3811:
3780:
3751:
3716:
3685:
3656:
3627:
3561:
3492:
3354:
3327:
3298:
3242:
3206:
3149:
3121:
3093:
3050:
3016:
2976:
2909:
2879:
2841:
2818:
2791:
2768:
2732:
2681:
2650:
2614:
2532:
2499:
2469:
2431:
2401:
2363:
2276:
2176:
2156:
2121:
2044:
2017:
1990:
1962:
1926:
1897:
1864:
1839:
1809:
1783:
1757:
1731:
1691:
1664:
1637:
1610:
1583:
1556:
1528:
1500:
1472:
1444:
1416:
1388:
1363:
1338:
1268:
1246:
1224:
1204:
1070:
1044:
1008:
969:
916:
878:
832:
794:
751:
731:
672:
629:
600:
543:
514:
389:
66:
6302:; Hayward, R.W.; Hoppes, D.D.; Hudson, R.P. (1957).
583:{\displaystyle {\hat {\mathcal {P}}}^{2}={\hat {1}}}
183:, are symmetric under parity. As established by the
5578:
5576:
5285:
behave like a mirrored image of the original clock.
4457:can be shown to have odd intrinsic parity, and all
2865:(German: even) and odd states by a subscript u for
5913:
5847:
5803:
5759:
5733:
5230:
5146:
5116:
5067:
5021:
4997:
4633:and antifermions have opposite intrinsic parity.)
4613:
4543:
4441:
4421:
4399:
4301:
4245:
4000:
3916:
3881:
3859:
3797:
3766:
3733:
3702:
3671:
3642:
3613:
3544:
3475:
3340:
3313:
3284:
3221:
3192:
3135:
3107:
3075:
3033:
2991:
2925:
2895:
2850:
2827:
2800:
2777:
2754:
2718:
2667:
2636:
2600:
2518:
2485:
2455:
2417:
2387:
2349:
2259:
2162:
2138:
2060:
2025:
1998:
1970:
1934:
1903:
1870:
1845:
1815:
1789:
1763:
1737:
1699:
1672:
1645:
1618:
1591:
1564:
1536:
1512:
1480:
1452:
1424:
1396:
1369:
1344:
1276:
1254:
1232:
1210:
1184:
1052:
1027:
986:
952:
899:
862:
815:
777:
737:
701:
658:
615:
582:
529:
480:
267:, physical configurations need to transform under
158:
6354:Wu Jianxiong: The first lady of physical sciences
6165:Roy, A. (2005). "Discovery of parity violation".
702:{\displaystyle {\hat {\mathcal {P}}}\phi =-\phi }
659:{\displaystyle {\hat {\mathcal {P}}}\phi =+\phi }
373:) which both transform as vectors under rotation.
5231:{\textstyle {\frac {(-1)(1)^{2}}{(1)^{2}}}=-1~,}
4998:{\displaystyle ~\mathbf {L} ={\boldsymbol {0}}~}
932:
848:
4063:as well as certain symmetric molecules such as
4011:Many-particle systems: atoms, molecules, nuclei
1316:is a different, but intimately related issue.
745:which defines the representation. For a matrix
590:. All Abelian groups have only one-dimensional
6030:(1959). "On the phase factors in inversions".
4122:while the latter are denoted by the subscript
4027:have parity (−1), where the exponent ℓ is the
2719:{\displaystyle {{\hat {\mathcal {P}}}'}^{2}=1}
6659:
5238:from which they concluded that the pion is a
3745:Some of the non-degenerate eigenfunctions of
3600:
3564:
3531:
3495:
3468:
3436:
3403:
3371:
3277:
3245:
3010:(symmetric) under a parity transformation if
222:a parity transformation; it is the same as a
8:
5676:"The symmetry groups of non-rigid molecules"
5559:(4th ed.). Prentice-Hall. p. 355.
5534:(4th ed.). Prentice-Hall. p. 163.
4838:, the discrete symmetry is also part of the
4794:is part of a continuous symmetry group then
3834:
3181:
3150:
3130:
3102:
4706:. Therefore, the parity operator satisfies
305:SO(3), are ordinary representations of the
6666:
6652:
6644:
6347:Wu jian xiong-wu li ke xue de si yi fu ren
5964:Cottingham, W.N.; Greenwood, D.A. (1986).
5320:An obscure 1928 experiment, undertaken by
4110:. The former are denoted by the subscript
1028:{\displaystyle \mathbf {F} =m\mathbf {a} }
214:equal to −1, and hence is distinct from a
6512:
6432:
6329:
6279:
5905:
5900:
5895:
5835:
5831:
5821:
5816:
5791:
5787:
5777:
5772:
5751:
5746:
5725:
5720:
5699:
5633:Bransden, B. H.; Joachain, C. J. (2003).
5617:
5204:
5186:
5161:
5159:
5130:
5102:
5080:
5045:
5014:
4987:
4979:
4974:
4603:
4592:
4583:
4578:
4569:
4558:
4556:
4527:
4509:
4503:
4502:
4487:
4472:
4471:
4469:
4434:
4414:
4412:
4383:
4372:
4363:
4358:
4343:
4332:
4330:
4283:
4281:
4280:
4266:
4265:
4258:
4207:
4205:
4204:
4202:
3973:
3971:
3970:
3969:
3946:
3935:
3933:
3932:
3929:
3903:
3901:
3900:
3898:
3874:
3826:
3815:
3813:
3812:
3810:
3784:
3782:
3781:
3779:
3753:
3752:
3750:
3720:
3718:
3717:
3715:
3689:
3687:
3686:
3684:
3658:
3657:
3655:
3629:
3628:
3626:
3599:
3598:
3587:
3585:
3584:
3570:
3569:
3563:
3562:
3560:
3530:
3529:
3518:
3516:
3515:
3501:
3500:
3494:
3493:
3491:
3467:
3466:
3460:
3442:
3441:
3435:
3434:
3428:
3402:
3401:
3395:
3377:
3376:
3370:
3369:
3358:
3356:
3355:
3353:
3332:
3326:
3300:
3299:
3297:
3276:
3275:
3269:
3251:
3250:
3244:
3243:
3241:
3208:
3207:
3205:
3173:
3162:
3161:
3156:
3148:
3122:
3120:
3094:
3092:
3060:
3049:
3020:
3018:
3017:
3015:
2983:
2979:
2978:
2975:
2917:
2908:
2887:
2878:
2840:
2817:
2790:
2767:
2737:
2735:
2734:
2731:
2704:
2688:
2686:
2685:
2683:
2680:
2654:
2652:
2651:
2649:
2619:
2617:
2616:
2613:
2591:
2586:
2578:
2574:
2569:
2558:
2556:
2555:
2537:
2535:
2534:
2531:
2504:
2498:
2474:
2468:
2456:{\displaystyle {\hat {\mathcal {P}}}^{2}}
2447:
2436:
2434:
2433:
2430:
2406:
2400:
2388:{\displaystyle {\hat {\mathcal {P}}}^{2}}
2379:
2368:
2366:
2365:
2362:
2334:
2322:
2302:
2298:
2292:
2281:
2279:
2278:
2275:
2239:
2229:
2224:
2216:
2215:
2195:
2191:
2180:
2178:
2177:
2175:
2155:
2125:
2123:
2122:
2120:
2049:
2043:
2018:
2016:
1991:
1989:
1963:
1961:
1927:
1925:
1896:
1863:
1838:
1808:
1782:
1756:
1730:
1692:
1690:
1665:
1663:
1638:
1636:
1611:
1609:
1584:
1582:
1557:
1555:
1529:
1527:
1505:
1504:
1499:
1473:
1471:
1445:
1443:
1417:
1415:
1389:
1387:
1362:
1337:
1269:
1267:
1247:
1245:
1225:
1223:
1203:
1170:
1159:
1142:
1120:
1105:
1104:
1095:
1087:
1075:
1071:
1069:
1045:
1043:
1020:
1009:
1007:
970:
968:
963:When the representation is restricted to
915:
877:
831:
793:
758:
750:
730:
676:
674:
673:
671:
633:
631:
630:
628:
607:
603:
602:
599:
569:
568:
559:
548:
546:
545:
542:
521:
517:
516:
513:
439:
403:
394:
388:
111:
75:
67:
65:
6501:Progress in Particle and Nuclear Physics
5505:, and is closely related to the flow of
5308:by expressing the weak interaction as a
168:It can also be thought of as a test for
5522:
5494:
5336:, because it implied parity violation.
1288:are invariant under parity because the
6369:
5970:. Cambridge University Press. p.
5117:{\displaystyle ~\left(-1\right)^{L}~.}
4504:
4473:
4253:, the Hamiltonian is parity invariant
3621:, then a non-degenerate eigenstate of
2755:{\displaystyle {\hat {\mathcal {P}}}'}
2637:{\displaystyle {\hat {\mathcal {P}}}'}
27:Symmetry of spatially mirrored systems
6132:
6130:
6000:The Quantum Theory of Fields Volume 1
4679:symmetries with charges equal to the
4625:are dealt with in the article on the
4429:denotes the momentum of a photon and
3917:{\displaystyle {\hat {\mathcal {P}}}}
3798:{\displaystyle {\hat {\mathcal {P}}}}
3774:are unaffected (invariant) by parity
3734:{\displaystyle {\hat {\mathcal {P}}}}
3703:{\displaystyle {\hat {\mathcal {P}}}}
3034:{\displaystyle {\hat {\mathcal {P}}}}
2668:{\displaystyle {\hat {\mathcal {P}}}}
2139:{\displaystyle {\hat {\mathcal {P}}}}
1262:are vectors, but the magnetic field,
7:
6577:Discrete symmetries and CP violation
6558:Introduction to High Energy Physics
6376:: CS1 maint: ignored ISBN errors (
3076:{\displaystyle V=V{\left(r\right)}}
1513:{\displaystyle \rho \,\mathbf {v} }
778:{\displaystyle R\in {\text{O}}(3),}
343:) which are rotationally invariant.
6598:Bigi, I. I.; Sanda, A. I. (2000).
5967:An introduction to nuclear physics
5304:. The Standard Model incorporates
2808:under a parity transformation are
1364:
953:{\displaystyle \rho (R)=\det(R)R.}
210:(in any number of dimensions) has
25:
4946:) and a negatively charged pion (
4763:, consider the general case when
4104:, or they are changed in sign by
3108:{\displaystyle |\varphi \rangle }
2785:. Wave functions with eigenvalue
1218:is a scalar, the electric field,
6345:Caijian, Jiang (1 August 1996).
5292:Although parity is conserved in
5274:
5260:
4988:
4980:
4604:
4593:
4579:
4570:
4562:
4559:
4528:
4488:
4415:
4384:
4373:
4359:
4344:
4336:
4333:
2992:{\displaystyle \mathbb {Z} _{2}}
2644:our parity operator, instead of
2019:
1992:
1964:
1928:
1711:(flow of electromagnetic power).
1693:
1666:
1639:
1612:
1585:
1558:
1530:
1506:
1474:
1446:
1418:
1390:
1292:of an axial vector is a vector.
1270:
1248:
1226:
1171:
1160:
1143:
1121:
1096:
1088:
1076:
1046:
1021:
1010:
907:, the fundamental representation
863:{\displaystyle \rho (R)=\det(R)}
616:{\displaystyle \mathbb {Z} _{2}}
530:{\displaystyle \mathbb {Z} _{2}}
175:All fundamental interactions of
68:
5409:Relativistic Heavy Ion Collider
4966:) in a state with zero orbital
4800:exists, but if it is part of a
4461:to have even intrinsic parity.
2963:Consequences of parity symmetry
2150:, in general acting on a state
6560:. Cambridge University Press.
6137:Muzzin, S.T. (19 March 2010).
5674:Longuet-Higgins, H.C. (1963).
5635:Physics of Atoms and Molecules
5509:oscillations through a medium.
5360:to try it. She needed special
5201:
5194:
5183:
5176:
5173:
5164:
4807:The Standard Model exhibits a
4608:
4597:
4574:
4566:
4538:
4524:
4498:
4481:
4394:
4377:
4354:
4340:
4288:
4271:
4212:
3978:
3940:
3908:
3827:
3820:
3789:
3758:
3725:
3694:
3663:
3634:
3592:
3575:
3523:
3506:
3447:
3382:
3363:
3305:
3256:
3213:
3174:
3167:
3157:
3136:{\displaystyle |\psi \rangle }
3123:
3095:
3025:
2742:
2693:
2659:
2624:
2563:
2542:
2441:
2373:
2286:
2185:
2130:
2107:of parity are one-dimensional.
1164:
1153:
1147:
1136:
1110:
987:{\displaystyle {\text{SO}}(3)}
981:
975:
941:
935:
926:
920:
888:
882:
857:
851:
842:
836:
804:
798:
769:
763:
681:
638:
574:
553:
436:
243:Representation theory of SU(2)
191:by Chinese-American scientist
108:
1:
6470:10.1080/10619127.2018.1495479
5662:NIST Atomic Spectrum Database
4883:, then the discrete symmetry
2115:. The parity transformation,
1284:is an axial vector. However,
285:of rotations, but only under
44:) is the flip in the sign of
6623:The Quantum Theory of Fields
5366:National Bureau of Standards
5350:electromagnetic interactions
4653:Fixing the global symmetries
4648:Parity in the Standard Model
4422:{\displaystyle \mathbf {p} }
3292:of orbital angular momentum
2926:{\displaystyle 1\sigma _{u}}
2896:{\displaystyle 1\sigma _{g}}
2026:{\displaystyle \mathbf {M} }
1999:{\displaystyle \mathbf {H} }
1971:{\displaystyle \mathbf {B} }
1935:{\displaystyle \mathbf {L} }
1700:{\displaystyle \mathbf {S} }
1673:{\displaystyle \mathbf {A} }
1646:{\displaystyle \mathbf {P} }
1619:{\displaystyle \mathbf {D} }
1592:{\displaystyle \mathbf {E} }
1565:{\displaystyle \mathbf {J} }
1537:{\displaystyle \mathbf {F} }
1481:{\displaystyle \mathbf {p} }
1453:{\displaystyle \mathbf {a} }
1425:{\displaystyle \mathbf {v} }
1408:of a particle in three-space
1397:{\displaystyle \mathbf {x} }
1277:{\displaystyle \mathbf {B} }
1255:{\displaystyle \mathbf {j} }
1233:{\displaystyle \mathbf {E} }
1053:{\displaystyle \mathbf {L} }
1002:Newton's equation of motion
823:, the trivial representation
189:National Bureau of Standards
179:, with the exception of the
6556:Perkins, Donald H. (2000).
6216:10.1007/978-4-431-77056-5_4
6119:(rev. ed.). New York:
5943:10.1103/PhysRevLett.86.1725
5848:{\displaystyle ^{2}P_{1/2}}
5804:{\displaystyle ^{2}P_{3/2}}
5427:Intrinsic parity of hadrons
4773:for some internal symmetry
4197:is invariant under parity,
3143:have the same parity, then
2105:irreducible representations
1628:electric displacement field
592:irreducible representations
206:A matrix representation of
6807:
6627:Cambridge University Press
6604:Cambridge University Press
6531:10.1016/j.ppnp.2019.05.001
5877:10.1103/PhysRevLett.52.267
5583:Andrew, A. V. (2006). "2.
5249:
4656:
3767:{\displaystyle {\hat {H}}}
3672:{\displaystyle {\hat {H}}}
3643:{\displaystyle {\hat {H}}}
3614:{\displaystyle {\bigl }=0}
3545:{\displaystyle {\bigl }=0}
3314:{\displaystyle {\vec {L}}}
3222:{\displaystyle {\hat {X}}}
2967:When parity generates the
2418:{\displaystyle e^{i\phi }}
2079:those associated with the
1038:However, angular momentum
900:{\displaystyle \rho (R)=R}
816:{\displaystyle \rho (R)=1}
287:projective representations
277:predicts that states in a
240:
6725:
6702:
6679:
6405:; Weinrich, R.M. (1957).
6208:Nishina Memorial Lectures
6202:Wu, Chien-Shiung (2008),
5701:10.1080/00268976300100501
5591:. Springer. p. 274.
5352:, it was untested in the
4629:, where it is shown that
4193:If one can show that the
4156:mixing) and give rise to
3710:or is changed in sign by
271:of every symmetry group.
237:Simple symmetry relations
6434:10.1103/PhysRev.105.1415
6349:
6331:10.1103/PhysRev.105.1413
5914:{\displaystyle _{2}^{+}}
4152:vibronic states (called
4029:azimuthal quantum number
2950:weak nuclear interaction
2008:auxiliary magnetic field
303:special orthogonal group
6581:Oxford University Press
6281:10.1103/PhysRev.104.254
6097:10.1103/PhysRev.95.1561
5555:Levine, Ira N. (1991).
5530:Levine, Ira N. (1991).
4325:annihilation operator:
4318:quantum electrodynamics
3679:is either invariant to
3321:with z-axis projection
2948:of nuclei, because the
2519:{\displaystyle e^{-iQ}}
717:Representations of O(3)
6674:C, P, and T symmetries
5915:
5849:
5805:
5761:
5735:
5734:{\displaystyle ^{127}}
5421:chiral magnetic effect
5232:
5148:
5118:
5069:
5068:{\displaystyle ~L=1~.}
5038:Fermi–Dirac statistics
5023:
4999:
4917:demonstrated that the
4615:
4545:
4443:
4423:
4401:
4322:canonical quantization
4303:
4247:
4002:
3918:
3883:
3861:
3799:
3768:
3735:
3704:
3673:
3644:
3615:
3546:
3477:
3342:
3315:
3286:
3223:
3194:
3137:
3109:
3077:
3035:
3002:In quantum mechanics,
2993:
2927:
2897:
2852:
2829:
2802:
2779:
2756:
2720:
2669:
2638:
2602:
2520:
2487:
2486:{\displaystyle e^{iQ}}
2457:
2419:
2389:
2351:
2261:
2164:
2140:
2108:
2062:
2061:{\displaystyle T_{ij}}
2027:
2000:
1972:
1936:
1905:
1872:
1847:
1817:
1791:
1765:
1739:
1701:
1674:
1647:
1620:
1593:
1566:
1538:
1514:
1482:
1454:
1426:
1398:
1371:
1346:
1278:
1256:
1234:
1212:
1186:
1054:
1029:
988:
954:
901:
864:
817:
779:
739:
703:
660:
617:
584:
531:
482:
160:
6621:Weinberg, S. (1995).
6575:Sozzi, M. S. (2008).
5916:
5850:
5806:
5762:
5736:
5240:pseudoscalar particle
5233:
5149:
5119:
5070:
5024:
5000:
4616:
4546:
4444:
4424:
4402:
4304:
4302:{\displaystyle \left}
4248:
4003:
3919:
3884:
3862:
3800:
3769:
3736:
3705:
3674:
3645:
3616:
3547:
3478:
3343:
3341:{\displaystyle L_{z}}
3316:
3287:
3224:
3195:
3138:
3110:
3078:
3036:
2994:
2928:
2898:
2853:
2851:{\displaystyle \pm 1}
2830:
2803:
2780:
2778:{\displaystyle \pm 1}
2757:
2721:
2670:
2639:
2603:
2521:
2488:
2458:
2420:
2390:
2352:
2262:
2165:
2163:{\displaystyle \psi }
2141:
2101:
2070:Maxwell stress tensor
2063:
2028:
2001:
1973:
1937:
1917:electromagnetic field
1906:
1904:{\displaystyle \rho }
1873:
1848:
1846:{\displaystyle \rho }
1818:
1792:
1766:
1740:
1702:
1675:
1655:electric polarization
1648:
1621:
1594:
1567:
1548:exerted on a particle
1539:
1515:
1483:
1455:
1427:
1399:
1372:
1370:{\displaystyle \Phi }
1347:
1314:parity transformation
1279:
1257:
1235:
1213:
1211:{\displaystyle \rho }
1198:, the charge density
1187:
1055:
1030:
989:
955:
902:
865:
818:
780:
740:
738:{\displaystyle \rho }
704:
661:
618:
585:
532:
483:
307:special unitary group
161:
38:parity transformation
18:Parity transformation
6771:Quantum field theory
6450:Nuclear Physics News
6121:New American Library
5894:
5815:
5771:
5760:{\displaystyle _{2}}
5745:
5719:
5585:Schrödinger equation
5315:hidden mirror sector
5158:
5147:{\displaystyle ~+1~}
5129:
5079:
5044:
5013:
4973:
4909:In 1954, a paper by
4555:
4468:
4442:{\displaystyle \pm }
4433:
4411:
4329:
4257:
4201:
4189:Quantum field theory
4077:sulphur hexafluoride
3928:
3897:
3873:
3809:
3778:
3749:
3714:
3683:
3654:
3625:
3559:
3490:
3352:
3325:
3296:
3240:
3204:
3147:
3119:
3091:
3048:
3014:
2974:
2907:
2877:
2839:
2816:
2789:
2766:
2730:
2679:
2648:
2612:
2530:
2497:
2467:
2429:
2399:
2361:
2274:
2174:
2154:
2119:
2094:Possible eigenvalues
2042:
2015:
1988:
1960:
1946:of a particle (both
1924:
1895:
1862:
1837:
1807:
1781:
1755:
1749:when an event occurs
1729:
1689:
1662:
1635:
1608:
1581:
1554:
1526:
1498:
1470:
1442:
1414:
1386:
1361:
1336:
1312:given below for the
1302:number of dimensions
1266:
1244:
1222:
1202:
1068:
1042:
1006:
967:
914:
876:
830:
792:
749:
729:
670:
666:, the other is odd,
627:
598:
541:
537:due to the relation
512:
387:
187:conducted at the US
177:elementary particles
64:
6761:Physical quantities
6523:2019PrPNP.107..200Z
6462:2019NPNew..29...26K
6425:1957PhRv..105.1415G
6322:1957PhRv..105.1413W
6272:1956PhRv..104..254L
6089:1954PhRv...95.1561C
6044:1959NCim...14..571F
5935:2001PhRvL..86.1725C
5910:
5869:1984PhRvL..52..267P
5692:1963MolPh...6..445L
5413:quark–gluon plasmas
5302:strong interactions
4718:for some choice of
4174:nuclear shell model
4073:xenon tetrafluoride
3889:is a constant, the
2812:, while eigenvalue
2270:One must then have
1286:Maxwell's equations
998:Classical mechanics
263:of higher rank. In
6740:Symmetry (physics)
6181:10.1007/BF02835140
6052:10.1007/BF02726388
5911:
5897:
5845:
5801:
5757:
5731:
5473:Molecular symmetry
5463:Electroweak theory
5417:STAR collaboration
5400:in the physics of
5228:
5144:
5114:
5065:
5019:
4995:
4905:Parity of the pion
4611:
4541:
4439:
4419:
4397:
4299:
4243:
4178:isotopes of oxygen
4061:diatomic molecules
3998:
3914:
3879:
3857:
3795:
3764:
3731:
3700:
3669:
3640:
3611:
3542:
3473:
3338:
3311:
3282:
3219:
3190:
3133:
3105:
3073:
3031:
2989:
2923:
2893:
2848:
2828:{\displaystyle -1}
2825:
2801:{\displaystyle +1}
2798:
2775:
2752:
2716:
2665:
2634:
2598:
2516:
2483:
2453:
2415:
2385:
2347:
2257:
2160:
2136:
2109:
2058:
2023:
1996:
1968:
1932:
1901:
1883:electric potential
1868:
1843:
1813:
1787:
1761:
1735:
1697:
1680:, electromagnetic
1670:
1643:
1616:
1589:
1562:
1534:
1510:
1478:
1450:
1422:
1394:
1367:
1342:
1274:
1252:
1230:
1208:
1182:
1180:
1050:
1025:
984:
950:
897:
860:
813:
775:
735:
724:group homomorphism
699:
656:
613:
580:
527:
478:
469:
430:
156:
147:
102:
6781:Conservation laws
6766:Quantum mechanics
6748:
6747:
6590:978-0-19-929666-8
6225:978-4-431-77055-8
5680:Molecular Physics
5648:978-0-582-35692-4
5598:978-0-387-25573-6
5557:Quantum Chemistry
5532:Quantum Chemistry
5224:
5211:
5143:
5134:
5110:
5084:
5061:
5049:
5022:{\displaystyle n}
4994:
4978:
4911:William Chinowsky
4802:discrete symmetry
4675:has three global
4291:
4274:
4215:
3981:
3943:
3911:
3882:{\displaystyle c}
3823:
3792:
3761:
3728:
3697:
3666:
3637:
3595:
3578:
3526:
3509:
3450:
3385:
3366:
3308:
3259:
3231:position operator
3216:
3170:
3028:
2952:violates parity.
2745:
2696:
2662:
2627:
2566:
2545:
2444:
2376:
2289:
2188:
2133:
2089:Quantum mechanics
1871:{\displaystyle V}
1816:{\displaystyle P}
1790:{\displaystyle E}
1764:{\displaystyle m}
1738:{\displaystyle t}
1345:{\displaystyle h}
1113:
973:
761:
684:
641:
577:
556:
505:Parity forms the
299:central extension
265:classical physics
197:radioactive decay
16:(Redirected from
6798:
6668:
6661:
6654:
6645:
6640:
6617:
6594:
6571:
6543:
6542:
6516:
6496:
6490:
6489:
6445:
6439:
6438:
6436:
6419:(4): 1415–1417.
6395:
6389:
6381:
6375:
6367:
6342:
6336:
6335:
6333:
6316:(4): 1413–1415.
6292:
6286:
6285:
6283:
6242:
6236:
6235:
6234:
6232:
6199:
6193:
6192:
6162:
6156:
6155:
6153:
6151:
6134:
6125:
6124:
6107:
6101:
6100:
6083:(6): 1561–1564.
6070:
6064:
6063:
6032:Il Nuovo Cimento
6020:
6014:
6013:
5996:Weinberg, Steven
5992:
5986:
5985:
5961:
5955:
5954:
5929:(9): 1725–1728.
5920:
5918:
5917:
5912:
5909:
5904:
5887:
5881:
5880:
5854:
5852:
5851:
5846:
5844:
5843:
5839:
5826:
5825:
5810:
5808:
5807:
5802:
5800:
5799:
5795:
5782:
5781:
5766:
5764:
5763:
5758:
5756:
5755:
5740:
5738:
5737:
5732:
5730:
5729:
5712:
5706:
5705:
5703:
5671:
5665:
5659:
5653:
5652:
5637:(2nd ed.).
5630:
5624:
5623:
5621:
5609:
5603:
5602:
5580:
5571:
5570:
5552:
5546:
5545:
5527:
5510:
5499:
5397:
5354:weak interaction
5306:parity violation
5294:electromagnetism
5278:
5264:
5246:Parity violation
5237:
5235:
5234:
5229:
5222:
5212:
5210:
5209:
5208:
5192:
5191:
5190:
5162:
5153:
5151:
5150:
5145:
5141:
5132:
5123:
5121:
5120:
5115:
5108:
5107:
5106:
5101:
5097:
5082:
5074:
5072:
5071:
5066:
5059:
5047:
5028:
5026:
5025:
5020:
5004:
5002:
5001:
4996:
4992:
4991:
4983:
4976:
4968:angular momentum
4965:
4964:
4963:
4962:
4955:
4954:
4945:
4943:
4942:
4935:
4934:
4915:Jack Steinberger
4900:
4893:
4891:
4886:
4882:
4871:
4857:
4855:
4850:
4848:
4843:
4837:
4816:
4811:symmetry, where
4810:
4799:
4798:
4793:
4789:
4788:
4785:
4781:
4776:
4772:
4771:
4767:
4762:
4760:
4752:
4746:
4742:
4738:
4733:
4729:
4725:
4721:
4717:
4712:
4705:
4696:
4687:
4670:
4669:
4620:
4618:
4617:
4612:
4607:
4596:
4588:
4587:
4582:
4573:
4565:
4550:
4548:
4547:
4542:
4531:
4517:
4516:
4508:
4507:
4491:
4477:
4476:
4453:. Similarly all
4451:intrinsic parity
4448:
4446:
4445:
4440:
4428:
4426:
4425:
4420:
4418:
4406:
4404:
4403:
4398:
4387:
4376:
4368:
4367:
4362:
4347:
4339:
4308:
4306:
4305:
4300:
4298:
4294:
4293:
4292:
4287:
4282:
4276:
4275:
4267:
4252:
4250:
4249:
4244:
4242:
4228:
4217:
4216:
4211:
4206:
4007:
4005:
4004:
3999:
3994:
3983:
3982:
3977:
3972:
3962:
3951:
3950:
3945:
3944:
3939:
3934:
3923:
3921:
3920:
3915:
3913:
3912:
3907:
3902:
3888:
3886:
3885:
3880:
3866:
3864:
3863:
3858:
3853:
3830:
3825:
3824:
3819:
3814:
3804:
3802:
3801:
3796:
3794:
3793:
3788:
3783:
3773:
3771:
3770:
3765:
3763:
3762:
3754:
3740:
3738:
3737:
3732:
3730:
3729:
3724:
3719:
3709:
3707:
3706:
3701:
3699:
3698:
3693:
3688:
3678:
3676:
3675:
3670:
3668:
3667:
3659:
3649:
3647:
3646:
3641:
3639:
3638:
3630:
3620:
3618:
3617:
3612:
3604:
3603:
3597:
3596:
3591:
3586:
3580:
3579:
3571:
3568:
3567:
3551:
3549:
3548:
3543:
3535:
3534:
3528:
3527:
3522:
3517:
3511:
3510:
3502:
3499:
3498:
3482:
3480:
3479:
3474:
3472:
3471:
3465:
3464:
3452:
3451:
3443:
3440:
3439:
3433:
3432:
3427:
3423:
3407:
3406:
3400:
3399:
3387:
3386:
3378:
3375:
3374:
3368:
3367:
3362:
3357:
3347:
3345:
3344:
3339:
3337:
3336:
3320:
3318:
3317:
3312:
3310:
3309:
3301:
3291:
3289:
3288:
3283:
3281:
3280:
3274:
3273:
3261:
3260:
3252:
3249:
3248:
3228:
3226:
3225:
3220:
3218:
3217:
3209:
3199:
3197:
3196:
3191:
3177:
3172:
3171:
3163:
3160:
3142:
3140:
3139:
3134:
3126:
3114:
3112:
3111:
3106:
3098:
3082:
3080:
3079:
3074:
3072:
3071:
3040:
3038:
3037:
3032:
3030:
3029:
3024:
3019:
2998:
2996:
2995:
2990:
2988:
2987:
2982:
2957:angular momentum
2932:
2930:
2929:
2924:
2922:
2921:
2902:
2900:
2899:
2894:
2892:
2891:
2857:
2855:
2854:
2849:
2834:
2832:
2831:
2826:
2807:
2805:
2804:
2799:
2784:
2782:
2781:
2776:
2762:has eigenvalues
2761:
2759:
2758:
2753:
2751:
2747:
2746:
2741:
2736:
2725:
2723:
2722:
2717:
2709:
2708:
2703:
2702:
2698:
2697:
2692:
2687:
2674:
2672:
2671:
2666:
2664:
2663:
2658:
2653:
2643:
2641:
2640:
2635:
2633:
2629:
2628:
2623:
2618:
2607:
2605:
2604:
2599:
2597:
2596:
2595:
2590:
2585:
2568:
2567:
2562:
2557:
2551:
2547:
2546:
2541:
2536:
2525:
2523:
2522:
2517:
2515:
2514:
2492:
2490:
2489:
2484:
2482:
2481:
2462:
2460:
2459:
2454:
2452:
2451:
2446:
2445:
2440:
2435:
2424:
2422:
2421:
2416:
2414:
2413:
2394:
2392:
2391:
2386:
2384:
2383:
2378:
2377:
2372:
2367:
2356:
2354:
2353:
2348:
2346:
2345:
2330:
2329:
2314:
2313:
2297:
2296:
2291:
2290:
2285:
2280:
2266:
2264:
2263:
2258:
2256:
2255:
2251:
2235:
2234:
2233:
2228:
2223:
2207:
2206:
2190:
2189:
2184:
2179:
2169:
2167:
2166:
2161:
2148:unitary operator
2145:
2143:
2142:
2137:
2135:
2134:
2129:
2124:
2067:
2065:
2064:
2059:
2057:
2056:
2032:
2030:
2029:
2024:
2022:
2005:
2003:
2002:
1997:
1995:
1977:
1975:
1974:
1969:
1967:
1954:) (axial vector)
1944:angular momentum
1941:
1939:
1938:
1933:
1931:
1910:
1908:
1907:
1902:
1877:
1875:
1874:
1869:
1852:
1850:
1849:
1844:
1822:
1820:
1819:
1814:
1796:
1794:
1793:
1788:
1770:
1768:
1767:
1762:
1744:
1742:
1741:
1736:
1706:
1704:
1703:
1698:
1696:
1682:vector potential
1679:
1677:
1676:
1671:
1669:
1652:
1650:
1649:
1644:
1642:
1625:
1623:
1622:
1617:
1615:
1598:
1596:
1595:
1590:
1588:
1571:
1569:
1568:
1563:
1561:
1543:
1541:
1540:
1535:
1533:
1519:
1517:
1516:
1511:
1509:
1487:
1485:
1484:
1479:
1477:
1459:
1457:
1456:
1451:
1449:
1431:
1429:
1428:
1423:
1421:
1403:
1401:
1400:
1395:
1393:
1376:
1374:
1373:
1368:
1351:
1349:
1348:
1343:
1283:
1281:
1280:
1275:
1273:
1261:
1259:
1258:
1253:
1251:
1239:
1237:
1236:
1231:
1229:
1217:
1215:
1214:
1209:
1191:
1189:
1188:
1183:
1181:
1174:
1163:
1146:
1128:
1124:
1115:
1114:
1106:
1099:
1091:
1079:
1059:
1057:
1056:
1051:
1049:
1034:
1032:
1031:
1026:
1024:
1013:
993:
991:
990:
985:
974:
971:
959:
957:
956:
951:
906:
904:
903:
898:
869:
867:
866:
861:
822:
820:
819:
814:
784:
782:
781:
776:
762:
759:
744:
742:
741:
736:
708:
706:
705:
700:
686:
685:
680:
675:
665:
663:
662:
657:
643:
642:
637:
632:
622:
620:
619:
614:
612:
611:
606:
589:
587:
586:
581:
579:
578:
570:
564:
563:
558:
557:
552:
547:
536:
534:
533:
528:
526:
525:
520:
487:
485:
484:
479:
474:
473:
435:
434:
399:
398:
372:
355:
342:
329:
181:weak interaction
165:
163:
162:
157:
152:
151:
107:
106:
71:
56:point reflection
42:parity inversion
21:
6806:
6805:
6801:
6800:
6799:
6797:
6796:
6795:
6786:Quantum numbers
6776:Nuclear physics
6751:
6750:
6749:
6744:
6721:
6698:
6675:
6672:
6637:
6620:
6614:
6597:
6591:
6574:
6568:
6555:
6552:
6547:
6546:
6498:
6497:
6493:
6447:
6446:
6442:
6412:Physical Review
6397:
6396:
6392:
6368:
6364:
6363:978-957132110-3
6351:
6344:
6343:
6339:
6309:Physical Review
6294:
6293:
6289:
6259:Physical Review
6244:
6243:
6239:
6230:
6228:
6226:
6201:
6200:
6196:
6175:(12): 164–175.
6164:
6163:
6159:
6149:
6147:
6136:
6135:
6128:
6111:Gardner, Martin
6109:
6108:
6104:
6076:Physical Review
6072:
6071:
6067:
6022:
6021:
6017:
6010:
5994:
5993:
5989:
5982:
5963:
5962:
5958:
5923:Phys. Rev. Lett
5892:
5891:
5889:
5888:
5884:
5857:Phys. Rev. Lett
5827:
5818:
5813:
5812:
5783:
5774:
5769:
5768:
5748:
5743:
5742:
5722:
5717:
5716:
5714:
5713:
5709:
5673:
5672:
5668:
5660:
5656:
5649:
5641:. p. 204.
5632:
5631:
5627:
5611:
5610:
5606:
5599:
5582:
5581:
5574:
5567:
5554:
5553:
5549:
5542:
5529:
5528:
5524:
5514:
5513:
5503:linear momentum
5500:
5496:
5486:
5449:
5429:
5395:
5358:Chien-Shiung Wu
5290:
5289:
5288:
5287:
5286:
5279:
5270:
5269:
5268:
5265:
5254:
5248:
5200:
5193:
5182:
5163:
5156:
5155:
5127:
5126:
5090:
5086:
5085:
5077:
5076:
5042:
5041:
5011:
5010:
4971:
4970:
4961:
4959:
4958:
4957:
4953:
4951:
4950:
4949:
4948:
4947:
4941:
4939:
4938:
4937:
4933:
4930:
4929:
4928:
4926:
4907:
4895:
4889:
4888:
4884:
4873:
4866:
4853:
4852:
4846:
4845:
4839:
4825:
4822:number operator
4812:
4808:
4796:
4795:
4791:
4786:
4783:
4779:
4778:
4774:
4769:
4765:
4764:
4758:
4757:
4748:
4740:
4736:
4735:
4731:
4727:
4723:
4719:
4708:
4707:
4701:
4699:electric charge
4692:
4683:
4665:
4664:
4661:
4655:
4650:
4577:
4553:
4552:
4501:
4466:
4465:
4431:
4430:
4409:
4408:
4357:
4327:
4326:
4264:
4260:
4255:
4254:
4232:
4218:
4199:
4198:
4191:
4184:
4170:
4128:and are called
4116:and are called
4042:Longuet-Higgins
4037:
4025:Atomic orbitals
4022:
4013:
3984:
3952:
3931:
3926:
3925:
3895:
3894:
3871:
3870:
3843:
3807:
3806:
3776:
3775:
3747:
3746:
3712:
3711:
3681:
3680:
3652:
3651:
3623:
3622:
3557:
3556:
3488:
3487:
3456:
3416:
3412:
3411:
3391:
3350:
3349:
3328:
3323:
3322:
3294:
3293:
3265:
3238:
3237:
3202:
3201:
3145:
3144:
3117:
3116:
3089:
3088:
3061:
3046:
3045:
3012:
3011:
2977:
2972:
2971:
2965:
2938:centrosymmetric
2913:
2905:
2904:
2883:
2875:
2874:
2872:
2837:
2836:
2814:
2813:
2787:
2786:
2764:
2763:
2733:
2728:
2727:
2684:
2682:
2677:
2676:
2646:
2645:
2615:
2610:
2609:
2570:
2533:
2528:
2527:
2500:
2495:
2494:
2470:
2465:
2464:
2432:
2427:
2426:
2402:
2397:
2396:
2364:
2359:
2358:
2335:
2318:
2303:
2277:
2272:
2271:
2244:
2240:
2211:
2196:
2172:
2171:
2152:
2151:
2117:
2116:
2096:
2091:
2086:
2045:
2040:
2039:
2013:
2012:
1986:
1985:
1958:
1957:
1922:
1921:
1893:
1892:
1860:
1859:
1835:
1834:
1805:
1804:
1779:
1778:
1753:
1752:
1727:
1726:
1719:
1714:
1709:Poynting vector
1687:
1686:
1660:
1659:
1633:
1632:
1606:
1605:
1579:
1578:
1574:current density
1552:
1551:
1524:
1523:
1496:
1495:
1490:linear momentum
1468:
1467:
1464:of the particle
1440:
1439:
1412:
1411:
1384:
1383:
1359:
1358:
1334:
1333:
1326:
1298:
1264:
1263:
1242:
1241:
1220:
1219:
1200:
1199:
1196:electrodynamics
1179:
1178:
1129:
1116:
1101:
1100:
1080:
1066:
1065:
1040:
1039:
1004:
1003:
1000:
965:
964:
912:
911:
910:pseudovectors:
874:
873:
828:
827:
826:pseudoscalars:
790:
789:
747:
746:
727:
726:
719:
668:
667:
625:
624:
601:
596:
595:
544:
539:
538:
515:
510:
509:
468:
467:
461:
460:
454:
453:
440:
429:
428:
422:
421:
415:
414:
404:
390:
385:
384:
377:One can define
367:
350:
337:
324:
269:representations
245:
239:
193:Chien-Shiung Wu
146:
145:
136:
135:
126:
125:
112:
101:
100:
94:
93:
87:
86:
76:
62:
61:
28:
23:
22:
15:
12:
11:
5:
6804:
6802:
6794:
6793:
6788:
6783:
6778:
6773:
6768:
6763:
6753:
6752:
6746:
6745:
6743:
6742:
6737:
6732:
6726:
6723:
6722:
6720:
6719:
6714:
6709:
6703:
6700:
6699:
6697:
6696:
6691:
6686:
6680:
6677:
6676:
6673:
6671:
6670:
6663:
6656:
6648:
6642:
6641:
6635:
6618:
6612:
6595:
6589:
6572:
6566:
6551:
6548:
6545:
6544:
6491:
6440:
6403:Lederman, L.M.
6390:
6362:
6350:吳健雄: 物理科學的第一夫人
6337:
6287:
6266:(1): 254–258.
6237:
6224:
6194:
6157:
6126:
6123:. p. 213.
6102:
6065:
6038:(3): 571–592.
6015:
6008:
5998:(1995). "16".
5987:
5980:
5956:
5908:
5903:
5899:
5882:
5863:(4): 267–269.
5842:
5838:
5834:
5830:
5824:
5820:
5798:
5794:
5790:
5786:
5780:
5776:
5754:
5750:
5728:
5724:
5707:
5686:(5): 445–460.
5666:
5654:
5647:
5625:
5604:
5597:
5572:
5565:
5547:
5540:
5521:
5520:
5512:
5511:
5493:
5492:
5485:
5482:
5481:
5480:
5475:
5470:
5465:
5460:
5455:
5448:
5445:
5428:
5425:
5388:L. M. Lederman
5346:Chen-Ning Yang
5280:
5273:
5272:
5271:
5266:
5259:
5258:
5257:
5256:
5255:
5247:
5244:
5227:
5221:
5218:
5215:
5207:
5203:
5199:
5196:
5189:
5185:
5181:
5178:
5175:
5172:
5169:
5166:
5140:
5137:
5113:
5105:
5100:
5096:
5093:
5089:
5064:
5058:
5055:
5052:
5018:
4990:
4986:
4982:
4960:
4952:
4940:
4931:
4906:
4903:
4673:Standard Model
4654:
4651:
4649:
4646:
4627:Dirac equation
4610:
4606:
4602:
4599:
4595:
4591:
4586:
4581:
4576:
4572:
4568:
4564:
4561:
4540:
4537:
4534:
4530:
4526:
4523:
4520:
4515:
4512:
4506:
4500:
4497:
4494:
4490:
4486:
4483:
4480:
4475:
4438:
4417:
4396:
4393:
4390:
4386:
4382:
4379:
4375:
4371:
4366:
4361:
4356:
4353:
4350:
4346:
4342:
4338:
4335:
4297:
4290:
4286:
4279:
4273:
4270:
4263:
4241:
4238:
4235:
4231:
4227:
4224:
4221:
4214:
4210:
4190:
4187:
4182:
4169:
4166:
4036:
4033:
4021:
4018:
4012:
4009:
3997:
3993:
3990:
3987:
3980:
3976:
3968:
3965:
3961:
3958:
3955:
3949:
3942:
3938:
3910:
3906:
3878:
3856:
3852:
3849:
3846:
3842:
3839:
3836:
3833:
3829:
3822:
3818:
3791:
3787:
3760:
3757:
3743:
3742:
3727:
3723:
3696:
3692:
3665:
3662:
3636:
3633:
3610:
3607:
3602:
3594:
3590:
3583:
3577:
3574:
3566:
3553:
3541:
3538:
3533:
3525:
3521:
3514:
3508:
3505:
3497:
3484:
3470:
3463:
3459:
3455:
3449:
3446:
3438:
3431:
3426:
3422:
3419:
3415:
3410:
3405:
3398:
3394:
3390:
3384:
3381:
3373:
3365:
3361:
3335:
3331:
3307:
3304:
3279:
3272:
3268:
3264:
3258:
3255:
3247:
3234:
3215:
3212:
3189:
3186:
3183:
3180:
3176:
3169:
3166:
3159:
3155:
3152:
3132:
3129:
3125:
3104:
3101:
3097:
3070:
3067:
3064:
3059:
3056:
3053:
3027:
3023:
2986:
2981:
2964:
2961:
2920:
2916:
2912:
2890:
2886:
2882:
2873:) is labelled
2870:
2847:
2844:
2824:
2821:
2810:even functions
2797:
2794:
2774:
2771:
2750:
2744:
2740:
2715:
2712:
2707:
2701:
2695:
2691:
2661:
2657:
2632:
2626:
2622:
2594:
2589:
2584:
2581:
2577:
2573:
2565:
2561:
2554:
2550:
2544:
2540:
2513:
2510:
2507:
2503:
2480:
2477:
2473:
2463:is an element
2450:
2443:
2439:
2412:
2409:
2405:
2382:
2375:
2371:
2344:
2341:
2338:
2333:
2328:
2325:
2321:
2317:
2312:
2309:
2306:
2301:
2295:
2288:
2284:
2254:
2250:
2247:
2243:
2238:
2232:
2227:
2222:
2219:
2214:
2210:
2205:
2202:
2199:
2194:
2187:
2183:
2159:
2132:
2128:
2113:quantum states
2095:
2092:
2090:
2087:
2085:
2084:
2073:
2055:
2052:
2048:
2037:
2021:
2010:
1994:
1983:
1982:(axial vector)
1980:magnetic field
1966:
1955:
1930:
1919:
1913:energy density
1900:
1890:
1867:
1857:
1855:charge density
1842:
1832:
1812:
1802:
1786:
1776:
1760:
1750:
1734:
1723:
1718:
1715:
1713:
1712:
1695:
1684:
1668:
1657:
1641:
1630:
1614:
1603:
1601:electric field
1587:
1576:
1560:
1549:
1532:
1521:
1508:
1503:
1493:
1476:
1465:
1448:
1437:
1420:
1409:
1392:
1381:
1366:
1356:
1341:
1330:
1325:
1322:
1297:
1294:
1272:
1250:
1240:, and current
1228:
1207:
1177:
1173:
1169:
1166:
1162:
1158:
1155:
1152:
1149:
1145:
1141:
1138:
1135:
1132:
1130:
1127:
1123:
1119:
1112:
1109:
1103:
1102:
1098:
1094:
1090:
1086:
1083:
1081:
1078:
1074:
1073:
1048:
1023:
1019:
1016:
1012:
999:
996:
983:
980:
977:
961:
960:
949:
946:
943:
940:
937:
934:
931:
928:
925:
922:
919:
908:
896:
893:
890:
887:
884:
881:
870:
859:
856:
853:
850:
847:
844:
841:
838:
835:
824:
812:
809:
806:
803:
800:
797:
774:
771:
768:
765:
757:
754:
734:
718:
715:
698:
695:
692:
689:
683:
679:
655:
652:
649:
646:
640:
636:
610:
605:
576:
573:
567:
562:
555:
551:
524:
519:
477:
472:
466:
463:
462:
459:
456:
455:
452:
449:
446:
445:
443:
438:
433:
427:
424:
423:
420:
417:
416:
413:
410:
409:
407:
402:
397:
393:
375:
374:
344:
275:Quantum theory
238:
235:
155:
150:
144:
141:
138:
137:
134:
131:
128:
127:
124:
121:
118:
117:
115:
110:
105:
99:
96:
95:
92:
89:
88:
85:
82:
81:
79:
74:
70:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6803:
6792:
6789:
6787:
6784:
6782:
6779:
6777:
6774:
6772:
6769:
6767:
6764:
6762:
6759:
6758:
6756:
6741:
6738:
6736:
6733:
6731:
6728:
6727:
6724:
6718:
6715:
6713:
6710:
6708:
6705:
6704:
6701:
6695:
6692:
6690:
6687:
6685:
6682:
6681:
6678:
6669:
6664:
6662:
6657:
6655:
6650:
6649:
6646:
6638:
6636:0-521-67053-5
6632:
6628:
6624:
6619:
6615:
6613:0-521-44349-0
6609:
6605:
6601:
6596:
6592:
6586:
6582:
6578:
6573:
6569:
6567:9780521621960
6563:
6559:
6554:
6553:
6549:
6540:
6536:
6532:
6528:
6524:
6520:
6515:
6510:
6506:
6502:
6495:
6492:
6487:
6483:
6479:
6475:
6471:
6467:
6463:
6459:
6455:
6451:
6444:
6441:
6435:
6430:
6426:
6422:
6418:
6414:
6413:
6408:
6404:
6400:
6394:
6391:
6388:
6387:957-13-2110-9
6384:
6379:
6373:
6365:
6359:
6355:
6348:
6341:
6338:
6332:
6327:
6323:
6319:
6315:
6311:
6310:
6305:
6301:
6297:
6291:
6288:
6282:
6277:
6273:
6269:
6265:
6261:
6260:
6255:
6251:
6247:
6241:
6238:
6227:
6221:
6217:
6213:
6209:
6205:
6198:
6195:
6190:
6186:
6182:
6178:
6174:
6170:
6169:
6161:
6158:
6146:
6145:
6140:
6133:
6131:
6127:
6122:
6118:
6117:
6112:
6106:
6103:
6098:
6094:
6090:
6086:
6082:
6078:
6077:
6069:
6066:
6061:
6057:
6053:
6049:
6045:
6041:
6037:
6033:
6029:
6025:
6019:
6016:
6011:
6009:9780521670531
6005:
6001:
5997:
5991:
5988:
5983:
5981:0-521-31960-9
5977:
5973:
5969:
5968:
5960:
5957:
5952:
5948:
5944:
5940:
5936:
5932:
5928:
5924:
5906:
5901:
5898:
5886:
5883:
5878:
5874:
5870:
5866:
5862:
5858:
5840:
5836:
5832:
5828:
5822:
5819:
5796:
5792:
5788:
5784:
5778:
5775:
5752:
5749:
5726:
5723:
5711:
5708:
5702:
5697:
5693:
5689:
5685:
5681:
5677:
5670:
5667:
5663:
5658:
5655:
5650:
5644:
5640:
5639:Prentice Hall
5636:
5629:
5626:
5620:
5615:
5608:
5605:
5600:
5594:
5590:
5586:
5579:
5577:
5573:
5568:
5566:0-205-12770-3
5562:
5558:
5551:
5548:
5543:
5541:0-205-12770-3
5537:
5533:
5526:
5523:
5519:
5518:
5508:
5504:
5498:
5495:
5491:
5490:
5483:
5479:
5476:
5474:
5471:
5469:
5468:Mirror matter
5466:
5464:
5461:
5459:
5456:
5454:
5451:
5450:
5446:
5444:
5442:
5438:
5434:
5426:
5424:
5422:
5418:
5414:
5410:
5405:
5403:
5399:
5391:
5389:
5385:
5381:
5377:
5373:
5369:
5367:
5363:
5359:
5355:
5351:
5347:
5343:
5342:Tsung-Dao Lee
5337:
5335:
5331:
5327:
5323:
5318:
5316:
5311:
5307:
5303:
5299:
5295:
5284:
5277:
5263:
5253:
5252:Wu experiment
5245:
5243:
5241:
5225:
5219:
5216:
5213:
5205:
5197:
5187:
5179:
5170:
5167:
5138:
5135:
5111:
5103:
5098:
5094:
5091:
5087:
5062:
5056:
5053:
5050:
5039:
5035:
5032:Neutrons are
5030:
5016:
5008:
4984:
4969:
4944:
4924:
4920:
4916:
4912:
4904:
4902:
4899:
4880:
4876:
4869:
4865:, which have
4864:
4861:
4842:
4836:
4832:
4828:
4823:
4820:
4815:
4805:
4803:
4754:
4751:
4745:
4716:
4711:
4704:
4700:
4695:
4691:
4690:lepton number
4686:
4682:
4681:baryon number
4678:
4674:
4668:
4660:
4652:
4647:
4645:
4643:
4639:
4634:
4632:
4628:
4624:
4600:
4589:
4584:
4535:
4532:
4521:
4518:
4513:
4510:
4495:
4492:
4484:
4478:
4462:
4460:
4459:axial-vectors
4456:
4455:vector bosons
4452:
4436:
4391:
4388:
4380:
4369:
4364:
4351:
4348:
4323:
4319:
4316:To show that
4314:
4312:
4295:
4277:
4268:
4261:
4239:
4236:
4233:
4229:
4225:
4222:
4219:
4196:
4188:
4186:
4179:
4175:
4167:
4165:
4163:
4159:
4155:
4151:
4150:
4145:
4144:
4139:
4138:
4133:
4132:
4127:
4126:
4121:
4120:
4115:
4114:
4109:
4108:
4103:
4102:
4096:
4095:
4090:
4089:
4084:
4083:
4078:
4074:
4070:
4066:
4062:
4057:
4055:
4054:
4049:
4048:
4043:
4034:
4032:
4030:
4026:
4019:
4017:
4010:
4008:
3995:
3991:
3988:
3985:
3966:
3963:
3959:
3956:
3953:
3947:
3892:
3876:
3867:
3854:
3850:
3847:
3844:
3840:
3837:
3831:
3755:
3660:
3631:
3608:
3605:
3581:
3572:
3554:
3539:
3536:
3512:
3503:
3485:
3461:
3457:
3453:
3444:
3429:
3424:
3420:
3417:
3413:
3408:
3396:
3392:
3388:
3379:
3333:
3329:
3302:
3270:
3266:
3262:
3253:
3235:
3232:
3210:
3187:
3184:
3178:
3164:
3153:
3127:
3099:
3086:
3085:
3084:
3068:
3065:
3062:
3057:
3054:
3051:
3043:
3009:
3005:
3000:
2984:
2970:
2969:Abelian group
2962:
2960:
2958:
2953:
2951:
2947:
2941:
2939:
2934:
2918:
2914:
2910:
2888:
2884:
2880:
2868:
2864:
2859:
2845:
2842:
2822:
2819:
2811:
2795:
2792:
2772:
2769:
2748:
2713:
2710:
2705:
2699:
2675:. Note that
2630:
2592:
2587:
2582:
2579:
2575:
2571:
2552:
2548:
2511:
2508:
2505:
2501:
2478:
2475:
2471:
2448:
2410:
2407:
2403:
2380:
2342:
2339:
2336:
2331:
2326:
2323:
2319:
2315:
2310:
2307:
2304:
2299:
2293:
2268:
2252:
2248:
2245:
2241:
2236:
2230:
2225:
2220:
2217:
2212:
2208:
2203:
2200:
2197:
2192:
2157:
2149:
2114:
2106:
2100:
2093:
2088:
2082:
2078:
2074:
2071:
2053:
2050:
2046:
2038:
2036:
2035:magnetization
2011:
2009:
1984:
1981:
1956:
1953:
1949:
1945:
1920:
1918:
1914:
1898:
1891:
1888:
1884:
1881:
1865:
1858:
1856:
1840:
1833:
1830:
1826:
1810:
1803:
1801:of a particle
1800:
1784:
1777:
1775:of a particle
1774:
1758:
1751:
1748:
1732:
1725:
1724:
1722:
1716:
1710:
1685:
1683:
1658:
1656:
1631:
1629:
1604:
1602:
1577:
1575:
1550:
1547:
1522:
1501:
1494:
1492:of a particle
1491:
1466:
1463:
1438:
1436:of a particle
1435:
1410:
1407:
1382:
1380:
1379:magnetic flux
1357:
1355:
1339:
1332:
1331:
1329:
1323:
1321:
1317:
1315:
1311:
1307:
1303:
1295:
1293:
1291:
1287:
1205:
1197:
1194:In classical
1192:
1175:
1167:
1156:
1150:
1139:
1133:
1131:
1125:
1117:
1107:
1092:
1084:
1082:
1063:
1036:
1017:
1014:
997:
995:
978:
947:
944:
938:
929:
923:
917:
909:
894:
891:
885:
879:
871:
854:
845:
839:
833:
825:
810:
807:
801:
795:
787:
786:
785:
772:
766:
755:
752:
732:
725:
716:
714:
712:
696:
693:
690:
687:
653:
650:
647:
644:
608:
593:
571:
565:
560:
522:
508:
507:abelian group
503:
501:
497:
493:
488:
475:
470:
464:
457:
450:
447:
441:
431:
425:
418:
411:
405:
400:
395:
391:
382:
380:
370:
365:
364:
363:pseudovectors
360:(also called
359:
358:axial vectors
353:
348:
345:
340:
335:
334:
333:pseudoscalars
327:
322:
319:
318:
317:
314:
312:
308:
304:
300:
295:
292:
288:
284:
280:
279:Hilbert space
276:
272:
270:
266:
262:
258:
254:
250:
244:
236:
234:
232:
227:
225:
224:180° rotation
221:
217:
213:
209:
204:
200:
198:
194:
190:
186:
185:Wu experiment
182:
178:
173:
171:
166:
153:
148:
142:
139:
132:
129:
122:
119:
113:
103:
97:
90:
83:
77:
72:
59:
57:
53:
50:
47:
43:
40:(also called
39:
35:
30:
19:
6717:CPT symmetry
6688:
6622:
6600:CP Violation
6599:
6576:
6557:
6504:
6500:
6494:
6456:(1): 26–31.
6453:
6449:
6443:
6416:
6410:
6399:Garwin, R.L.
6393:
6353:
6346:
6340:
6313:
6307:
6290:
6263:
6257:
6240:
6229:, retrieved
6207:
6197:
6172:
6166:
6160:
6148:. Retrieved
6142:
6115:
6105:
6080:
6074:
6068:
6035:
6031:
6028:Weinberg, S.
6024:Feinberg, G.
6018:
5999:
5990:
5966:
5959:
5926:
5922:
5885:
5860:
5856:
5710:
5683:
5679:
5669:
5657:
5634:
5628:
5607:
5588:
5556:
5550:
5531:
5525:
5516:
5515:
5497:
5488:
5487:
5458:CP violation
5430:
5406:
5392:
5384:R. L. Garwin
5370:
5338:
5330:Hermann Weyl
5319:
5305:
5291:
5282:
5036:and so obey
5031:
4908:
4897:
4878:
4874:
4867:
4840:
4834:
4830:
4826:
4813:
4806:
4755:
4749:
4743:
4714:
4709:
4702:
4693:
4684:
4666:
4662:
4635:
4463:
4315:
4195:vacuum state
4192:
4171:
4164:transitions
4161:
4157:
4153:
4148:
4147:
4142:
4141:
4136:
4135:
4130:
4129:
4124:
4123:
4118:
4117:
4112:
4111:
4106:
4105:
4100:
4099:
4093:
4092:
4087:
4086:
4081:
4080:
4058:
4052:
4051:
4046:
4045:
4038:
4023:
4014:
3868:
3744:
3236:For a state
3004:Hamiltonians
3001:
2966:
2954:
2942:
2935:
2866:
2862:
2860:
2269:
2170:as follows:
2110:
2076:
1720:
1462:acceleration
1327:
1318:
1313:
1309:
1305:
1301:
1299:
1193:
1062:axial vector
1037:
1001:
962:
720:
504:
499:
495:
491:
489:
383:
378:
376:
368:
361:
357:
351:
346:
338:
331:
325:
320:
315:
296:
290:
289:. The word
273:
246:
228:
219:
207:
205:
201:
174:
167:
60:
45:
41:
37:
31:
29:
6712:CP symmetry
6507:: 200–236.
5326:weak decays
1853:, electric
1572:, electric
1520:, mass flow
379:reflections
212:determinant
6755:Categories
6694:T-symmetry
6689:P-symmetry
6684:C-symmetry
6514:1906.11413
6250:Yang, C.N.
5484:References
5478:T-symmetry
5453:C-symmetry
5250:See also:
4697:, and the
4657:See also:
4642:spin group
4154:ortho-para
3891:eigenvalue
2946:beta decay
2081:weak force
291:projective
241:See also:
52:coordinate
6791:Asymmetry
6735:Pin group
6730:Chirality
6539:181517015
6486:133308325
6478:1061-9127
6372:cite book
6300:Ambler, E
6246:Lee, T.D.
6231:29 August
6189:124880732
6168:Resonance
6113:(1969) .
6060:120498009
5619:0811.3403
5517:Citations
5489:Footnotes
5439:decay to
5437:rho meson
5380:cobalt-60
5362:cryogenic
5322:R. T. Cox
5217:−
5168:−
5092:−
5005:into two
4863:neutrinos
4747:for some
4601:−
4522:ϕ
4511:−
4485:−
4479:ϕ
4437:±
4392:±
4381:−
4352:±
4289:^
4272:^
4213:^
4131:ungerade.
4035:Molecules
3989:ψ
3979:^
3957:ψ
3941:^
3909:^
3848:ψ
3835:⟩
3832:ψ
3821:^
3790:^
3759:^
3726:^
3695:^
3664:^
3635:^
3593:^
3576:^
3524:^
3507:^
3448:→
3418:−
3383:→
3364:^
3306:→
3257:→
3214:^
3182:⟩
3179:ψ
3168:^
3154:φ
3151:⟨
3131:⟩
3128:ψ
3103:⟩
3100:φ
3026:^
3008:invariant
2915:σ
2885:σ
2843:±
2820:−
2770:±
2743:^
2694:^
2660:^
2625:^
2576:−
2564:^
2553:≡
2543:^
2506:−
2442:^
2411:ϕ
2374:^
2332:ψ
2327:ϕ
2300:ψ
2287:^
2246:−
2237:ψ
2221:ϕ
2193:ψ
2186:^
2158:ψ
2131:^
1899:ρ
1841:ρ
1827:(rate of
1502:ρ
1365:Φ
1206:ρ
1157:−
1151:×
1140:−
1111:^
1093:×
918:ρ
880:ρ
872:vectors:
834:ρ
796:ρ
788:scalars:
756:∈
733:ρ
697:ϕ
694:−
688:ϕ
682:^
654:ϕ
645:ϕ
639:^
575:^
554:^
448:−
437:↦
249:rotations
170:chirality
140:−
130:−
120:−
109:↦
6296:Wu, C.S.
6252:(1956).
6150:5 August
5951:11290233
5855:Limit".
5447:See also
5034:fermions
5007:neutrons
4923:deuteron
4860:Majorana
4638:fermions
4631:fermions
4551:, since
4240:⟩
4226:⟩
4119:gerade,
4065:ethylene
3992:⟩
3960:⟩
3851:⟩
3469:⟩
3404:⟩
3278:⟩
3042:commutes
2867:ungerade
2749:′
2700:′
2631:′
2549:′
1434:velocity
1406:position
1354:helicity
381:such as
216:rotation
6550:Sources
6519:Bibcode
6458:Bibcode
6421:Bibcode
6318:Bibcode
6268:Bibcode
6144:PhysOrg
6085:Bibcode
6040:Bibcode
5931:Bibcode
5865:Bibcode
5767:at the
5688:Bibcode
5298:gravity
4819:fermion
4817:is the
4623:spinors
4069:benzene
3348:, then
3229:is the
2726:and so
2146:, is a
1948:orbital
1915:of the
1887:voltage
498:-, and
347:vectors
321:scalars
311:spinors
261:tensors
257:vectors
253:scalars
49:spatial
34:physics
6633:
6610:
6587:
6564:
6537:
6484:
6476:
6385:
6360:
6222:
6187:
6058:
6006:
5978:
5949:
5645:
5595:
5563:
5538:
5433:hadron
5398:puzzle
5376:Ambler
5310:chiral
5223:
5142:
5133:
5109:
5083:
5060:
5048:
4993:
4977:
4956:π
4896:±
4849:= (−1)
4750:α
4728:γ
4726:, and
4724:β
4720:α
4688:, the
4407:where
4168:Nuclei
3869:where
3200:where
2863:gerade
2425:. If
2077:except
2068:, the
2006:, the
1978:, the
1942:, the
1880:scalar
1799:energy
1797:, the
1771:, the
1745:, the
1707:, the
1626:, the
1599:, the
1544:, the
1488:, the
1460:, the
1432:, the
1404:, the
1060:is an
594:. For
356:) and
330:) and
259:, and
247:Under
6535:S2CID
6509:arXiv
6482:S2CID
6352:[
6185:S2CID
6056:S2CID
5614:arXiv
5507:sound
5441:pions
5402:kaons
5334:Pauli
4790:. If
4636:With
4158:ortho
4020:Atoms
1831:done)
1825:power
1546:force
711:phase
283:group
6631:ISBN
6608:ISBN
6585:ISBN
6562:ISBN
6474:ISSN
6383:ISBN
6378:link
6358:ISBN
6233:2021
6220:ISBN
6152:2011
6004:ISBN
5976:ISBN
5947:PMID
5643:ISBN
5593:ISBN
5561:ISBN
5536:ISBN
5344:and
5296:and
4919:pion
4913:and
4885:(−1)
4872:and
4809:(−1)
4677:U(1)
4659:(−1)
4311:good
4162:para
4146:and
4075:and
3115:and
3006:are
1952:spin
1950:and
1829:work
1773:mass
1747:time
1717:Even
1310:even
1290:curl
371:= +1
354:= −1
341:= −1
328:= +1
231:even
36:, a
6527:doi
6505:107
6466:doi
6429:doi
6417:105
6326:doi
6314:105
6276:doi
6264:104
6212:doi
6177:doi
6093:doi
6048:doi
5939:doi
5921:".
5873:doi
5727:127
5696:doi
5587:".
5396:τ–θ
5283:not
5029:).
4892:= 1
4881:= 0
4870:= 1
4856:= 1
4761:= 1
4183:5/2
4067:,
4050:or
3893:of
3555:If
3486:If
3087:If
1324:Odd
1308:or
1306:odd
933:det
849:det
494:-,
366:) (
220:not
58:):
46:one
32:In
6757::
6707:CP
6629:.
6625:.
6606:.
6583:.
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5372:Wu
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4768:=
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396:x
392:V
369:P
352:P
349:(
339:P
336:(
326:P
323:(
208:P
154:.
149:)
143:z
133:y
123:x
114:(
104:)
98:z
91:y
84:x
78:(
73::
69:P
20:)
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