31:
3512:
2006:, the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.
61:
1577:
4573:
3767:
1172:
2111:; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A
3779:
2466:
phonons, are associated with slow density fluctuations of the crystal's atoms. The associated
Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, NambuâGoldstone modes are typically massless and propagate at a constant velocity.
1533:, if two outcomes are considered, the probability distributions of a pair of outcomes can be different. For example in an electric field, the forces on a charged particle are different in different directions, so the rotational symmetry is explicitly broken by the electric field which does not have this symmetry.
2339:.) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide the unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional
2031:
model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to
2377:
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are
2500:
with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state.
2469:
An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of NambuâGoldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order
2042:
Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring
2465:
Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) NambuâGoldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as
1522:
transformation (such as translation or rotation), so that any pair of outcomes differing only by that transformation have the same probability distribution. For example if measurements of an observable at any two different positions have the same probability distribution, the observable has
2249:
states that local gauge symmetries can never be spontaneously broken. Rather, after gauge fixing, the global symmetry (or redundancy) can be broken in a manner formally resembling spontaneous symmetry breaking. One important consequence of the distinction between true symmetries and
2254:, is that the massless NambuâGoldstone resulting from spontaneous breaking of a gauge symmetry are absorbed in the description of the gauge vector field, providing massive vector field modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.
2501:
Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the
2470:
parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)
1547:
Typically, when spontaneous symmetry breaking occurs, the observable properties of the system change in multiple ways. For example the density, compressibility, coefficient of thermal expansion, and specific heat will be expected to change when a liquid becomes a solid.
2043:
friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite
2347:
by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".) Dynamical breaking of gauge symmetries is often due to creation of a
2024:, the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.
2089:
is an example of spontaneous symmetry breaking when both balloons are initially inflated to the local maximum pressure. When some air flows from one balloon into the other, the pressure in both balloons will drop, making the system more stable in the asymmetric
2520:. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.
2054:
over an infinite horizontal plane. This system has all the symmetries of the
Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough,
2118:
An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called
1572:
this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.
2461:
Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.
2481:, have been shown to break translational and rotational symmetries. It was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration â i.e., breaks
1719:
2323:
Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the
2617:
of CP symmetry in the weak interactions. This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.
45:), the overall "rules" remain symmetric, but the symmetric "sombrero" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.
2082:
from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.
1567:
Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may
2368:
is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.
2315:
Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e.,
2306:
of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.
2129:(that we know of) breaks the symmetry in the equations. By the nature of spontaneous symmetry breaking, different portions of the early Universe would break symmetry in different directions, leading to
2215:, whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.
1855:
2538:, and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the
2021:
1932:
2397:. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.
1981:
would have exactly the same energy, and the defining equations respect the symmetry but the ground state (vacuum) of the theory breaks the symmetry, implying the existence of a massless
3397:
1502:. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.
3817:
3349:
Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken
Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2 Interscience Publishers, New York. pp. 567â708
2911:
Muñoz-Vega, R.; GarcĂa-Quiroz, A.; LĂłpez-ChĂĄvez, Ernesto; Salinas-HernĂĄndez, EncarnaciĂłn (2012). "Spontaneous symmetry breakdown in non-relativistic quantum mechanics".
3344:
International
Journal of Modern Physics A: The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles
1764:
1611:
2281:
predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge. In addition, fermions develop mass consistently.
4370:
1643:
1458:
3541:
1147:
3048:
Jeannerot, Rachel; Rocher, Jonathan; Sakellariadou, Mairi (24 November 2003). "How generic is cosmic string formation in supersymmetric grand unified theories".
2389:
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as
4018:
3649:
2292:) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the
2565:), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a
2742:
Note that (as in fundamental Higgs driven spontaneous gauge symmetry breaking) the term "symmetry breaking" is a misnomer when applied to gauge symmetries.
1252:
230:
2496:
For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore
2628:
1653:
4541:
3526:
2245:
of metals and the origin of particle masses in the standard model of particle physics. The term "spontaneous symmetry breaking" is a misnomer here as
1985:, the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.
2709:
270:
2261:
gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The
4553:
3867:
2078:). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria,
3390:
2597:, won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically
4237:
3810:
4171:
3644:
3032:
2153:
and the dynamics of the theory. For example, Higgs symmetry breaking may have created primordial cosmic strings as a byproduct. Hypothetical
3307:
For a pedagogic introduction to electroweak symmetry breaking with step by step derivations, not found in texts, of many key relations, see
4094:
1005:
3727:
3333:
1451:
3215:
Kohlstedt, K.L.; Vernizzi, G.; Solis, F.J.; Olvera de la Cruz, M. (2007). "Spontaneous
Chirality via Long-range Electrostatic Forces".
2512:, but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate
1286:
3383:
1140:
3783:
2161:, creating difficulties for GUT unless monopoles (along with any GUT domain walls) are expelled from our observable Universe through
3840:
3803:
3551:
3355:
2825:
2798:
2725:
2582:
1294:
1214:
775:
2382:. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter â including nematic phases of
3950:
3732:
2331:
Dynamical breaking of a gauge symmetry is subtler. In conventional spontaneous gauge symmetry breaking, there exists an unstable
4217:
4212:
2039:, there is a condensed-matter collective field Ï, which acts as the order parameter breaking the electromagnetic gauge symmetry.
4612:
4508:
3935:
3162:(2010). "Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order".
73:
4192:
1562:
30:
4520:
3692:
2771:
2390:
2115:. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.
1541:
1444:
3339:
The
History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles
1526:
Spontaneous symmetry breaking occurs when this relation breaks down, while the underlying physical laws remain symmetrical.
338:
4602:
4498:
4275:
4197:
3980:
3850:
3583:
3328:
2704:
1778:
1133:
147:
4232:
1219:
4597:
4166:
4161:
4132:
3845:
3742:
2602:
875:
805:
177:
4207:
2458:
when the
Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.
1204:
333:
4300:
2546:
in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear)
2274:
1617:
In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative
1209:
275:
4117:
1886:
1224:
1540:
can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the
4576:
4338:
4146:
2614:
1530:
985:
182:
4069:
4000:
2694:
2502:
2288:
of elementary particle interactions requires the existence of a number of particles. However, some particles (the
2208:
323:
4360:
4227:
4151:
4112:
4043:
3893:
3697:
2405:
The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the
2317:
2120:
1622:
1491:
4427:
4407:
4397:
4387:
4343:
3918:
3702:
2653:
2638:
2598:
2528:
2357:
2174:
1278:
810:
440:
285:
250:
3616:
800:
4622:
4607:
4536:
4122:
4084:
4048:
3771:
3484:
3474:
3217:
2678:
2336:
2075:
1340:
1262:
1186:
1085:
555:
363:
358:
220:
4447:
4222:
4202:
4127:
4038:
3995:
3489:
3462:
2586:
2361:
2188:
2158:
2142:
2086:
955:
935:
435:
368:
280:
245:
127:
4472:
3985:
3965:
3737:
3611:
3578:
2594:
2527:. If there is a field (often a background field) which acquires an expectation value (not necessarily a
2241:, the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the
1357:
1163:
845:
705:
401:
265:
3888:
3279:
1998:
materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the
1970:
symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of
4503:
4432:
4377:
4107:
3930:
3687:
3626:
3621:
3595:
3442:
3236:
3181:
3124:
3067:
2987:
2930:
2877:
2720:
2663:
2349:
2278:
2246:
2192:
2154:
1645:, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,
1486:
state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the
1400:
1090:
870:
406:
260:
172:
52:
2965:
4488:
4457:
4402:
4382:
4290:
4247:
4102:
4028:
3955:
3945:
3857:
3654:
3106:
2394:
2379:
2184:
2146:
2067:
1618:
1515:
1487:
1475:
1395:
1385:
1197:
1100:
815:
545:
430:
3343:
3313:
3308:
720:
595:
4417:
4315:
4023:
3970:
3862:
3682:
3452:
3371:
University of
Cambridge, David Tong: Lectures on Quantum Field Theory for masters level students.
3260:
3226:
3197:
3171:
3102:
3057:
3003:
2977:
2946:
2920:
2893:
2688:
2633:
2497:
2228:
2130:
2032:
notice broken symmetries suggests why it took so long for us to discover electroweak unification.
1536:
Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple
1519:
1499:
1483:
1270:
1110:
1035:
965:
850:
835:
765:
730:
485:
445:
235:
197:
152:
140:
117:
112:
4548:
3365:
680:
4617:
4558:
4467:
4437:
4365:
4328:
4323:
4305:
4270:
4260:
3975:
3940:
3923:
3826:
3568:
3351:
3252:
3140:
3115:
3028:
2850:
2821:
2815:
2794:
2788:
2767:
2715:
2606:
2570:
2474:
2473:
Other long-range interacting systems, such as cylindrical curved surfaces interacting via the
2421:
2406:
2365:
2303:
2242:
2071:
2036:
2003:
1767:
1740:
1587:
1576:
1511:
1479:
1420:
1362:
1065:
995:
880:
785:
725:
660:
630:
600:
460:
455:
300:
225:
215:
107:
3092:
A Brief
History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73â74.
2761:
2542:
does not obey the initial symmetry (which would keep it invariant, in the linearly realized
2277:. At energies much greater than 100 GeV, all these particles behave in a similar manner. The
2195:
describing these interactions, and is responsible for the bulk of the mass (over 99%) of the
17:
4285:
4280:
4137:
4033:
3747:
3494:
3479:
3420:
3244:
3189:
3132:
3075:
2995:
2938:
2885:
2699:
2610:
2478:
2353:
2325:
2266:
2162:
2100:
1537:
1415:
1390:
1239:
1105:
1020:
1000:
970:
920:
745:
740:
735:
620:
605:
535:
240:
167:
157:
92:
1628:
1510:
By definition, spontaneous symmetry breaking requires the existence of physical laws (e.g.
4515:
4442:
4422:
4392:
4355:
4350:
4255:
4079:
3669:
3536:
3110:
2683:
2668:
2658:
2551:
2534:) which is not invariant under the symmetry in question, we say that the system is in the
2524:
2340:
2293:
2238:
2224:
2180:
2056:
2044:
2010:
1982:
1495:
1405:
1367:
1347:
1050:
1045:
1015:
1010:
980:
940:
910:
890:
795:
690:
685:
650:
635:
610:
590:
570:
500:
490:
411:
373:
290:
255:
87:
65:
60:
2999:
3240:
3185:
3128:
3071:
2991:
2934:
2881:
41:), the ball settles in the center, and the result is symmetric. At lower energy levels (
4493:
4462:
4452:
4074:
4064:
3898:
3707:
3406:
2590:
2509:
2383:
2344:
2332:
2289:
2285:
2262:
2234:
2150:
2138:
2108:
1410:
1317:
1229:
1181:
1075:
1025:
945:
930:
915:
895:
865:
860:
855:
840:
830:
825:
790:
780:
710:
645:
615:
550:
515:
505:
480:
351:
318:
192:
2179:
Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the
4591:
4412:
4265:
4156:
3990:
3960:
3913:
3677:
3636:
3348:
3159:
3007:
2950:
2897:
2843:
2535:
2104:
1999:
1967:
1080:
1070:
1060:
1055:
975:
960:
760:
755:
585:
580:
540:
510:
475:
465:
396:
391:
3264:
3201:
4295:
3908:
3903:
3659:
3590:
3499:
3457:
3447:
2643:
2566:
2539:
2482:
2296:
to give these particles mass. It also suggests the presence of a new particle, the
2233:
The strong, weak, and electromagnetic forces can all be understood as arising from
2134:
1714:{\displaystyle {\mathcal {L}}=\partial ^{\mu }\phi \partial _{\mu }\phi -V(\phi ).}
1430:
1171:
1115:
1040:
925:
900:
885:
820:
700:
695:
575:
565:
560:
525:
520:
495:
450:
328:
295:
122:
102:
3248:
2787:
Arodz, Henryk; Dziarmaga, Jacek; Zurek, Wojciech Hubert, eds. (30 November 2003).
3370:
3022:
4333:
3573:
3467:
3435:
3430:
3323:
3024:
Dreams of a Final Theory: The
Scientist's Search for the Ultimate Laws of Nature
2673:
2558:
2297:
2257:
In the standard model of particle physics, spontaneous symmetry breaking of the
2079:
2028:
2014:
1995:
1425:
1327:
1322:
1312:
1095:
1030:
990:
950:
905:
770:
675:
670:
655:
640:
625:
3193:
3079:
3334:
History of EnglertâBroutâHiggsâGuralnikâHagenâKibble Mechanism on Scholarpedia
2648:
2070:
is increased gradually from rest, the bead will initially stay at its initial
750:
665:
530:
470:
162:
97:
3366:
The Royal Society Publishing: Spontaneous symmetry breaking in gauge theories
3318:
3136:
2424:, the energy of the system is invariant under inversion of the magnetization
4187:
3883:
2562:
3256:
3144:
2589:
to three scientists for their work in subatomic physics symmetry breaking.
1766:
that the symmetry breaking is triggered. An example of a potential, due to
3360:
3324:
In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking
3752:
2485:
2196:
2063:
1581:
1352:
715:
2335:
in the theory, which drives the vacuum to a symmetry-broken phase (i.e,
3425:
3062:
2889:
2613:, shared the other half of the prize for discovering the origin of the
2204:
1875:
2942:
3113:(1990). "Minimal dynamical symmetry breaking of the standard model".
2270:
2200:
3795:
3361:
Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey
2865:
2062:
Consider a bead on a circular hoop that is rotated about a vertical
1974:), this symmetry will appear to be lost, or "spontaneously broken".
3329:
EnglertâBroutâHiggsâGuralnikâHagenâKibble Mechanism on Scholarpedia
2982:
3338:
3231:
3176:
2925:
2212:
2051:
1575:
1234:
29:
3375:
2573:, although a classical solution may break a continuous symmetry.
2199:, and thus of all common matter, as it converts very light bound
2013:, but the solid itself spontaneously breaks this group down to a
2386:, charge- and spin-density waves, superfluids, and many others.
2237:, which is a redundancy in the description of the symmetry. The
2017:. The displacement and the orientation are the order parameters.
1959:. The system also has an unstable vacuum state corresponding to
3799:
3379:
3309:
http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf
2550:. Normally, in the absence of the Higgs mechanism, massless
1659:
3319:
Physical Review Letters â 50th Anniversary Milestone Papers
2107:
particles are normally specified by field equations with
2009:
The laws describing a solid are invariant under the full
2002:, which measures the magnetic dipole density. Above the
2211:
in this spontaneous symmetry breaking process are the
2074:
at the bottom of the hoop (intuitively stable, lowest
2845:
Bright Air, Brilliant Fire: On the Matter of the Mind
2763:
Dynamical Symmetry Breaking in Quantum Field Theories
1889:
1781:
1743:
1656:
1631:
1590:
1850:{\displaystyle V(\phi )=-5|\phi |^{2}+|\phi |^{4}\,}
4529:
4481:
4314:
4246:
4180:
4093:
4057:
4011:
3876:
3833:
3720:
3668:
3635:
3604:
3561:
3550:
3519:
3413:
2817:
Bubbles, Voids and Bumps in Time: The New Cosmology
2866:"Field theories with " Superconductor " solutions"
2842:
2020:General relativity has a Lorentz symmetry, but in
1926:
1874:This potential has an infinite number of possible
1849:
1758:
1713:
1637:
1605:
2557:The symmetry group can be discrete, such as the
2523:The crucial concept in physics theories is the
1927:{\displaystyle \phi ={\sqrt {5/2}}e^{i\theta }}
3542:Mathematical formulation of the Standard Model
2265:are the elementary particles that mediate the
3811:
3391:
2508:When a theory is symmetric with respect to a
1452:
1141:
8:
2820:. Cambridge University Press. p. 125.
2378:oriented in a specific direction, breaking
2284:Without spontaneous symmetry breaking, the
2059:will form, breaking the Euclidean symmetry.
3818:
3804:
3796:
3558:
3398:
3384:
3376:
2966:"History of electroweak symmetry breaking"
2629:Autocatalytic reactions and order creation
2451:. The symmetry is spontaneously broken as
2420:is the external magnetic field. Below the
1459:
1445:
1170:
1159:
1148:
1134:
59:
48:
27:Symmetry breaking through the vacuum state
3230:
3175:
3061:
2981:
2924:
2710:Spontaneous absolute asymmetric synthesis
2187:in particle physics. It is a property of
1915:
1901:
1896:
1888:
1846:
1840:
1835:
1826:
1817:
1812:
1803:
1780:
1770:is illustrated in the graph at the left.
1742:
1684:
1671:
1658:
1657:
1655:
1630:
1589:
35:Spontaneous symmetry breaking illustrated
2814:Cornell, James, ed. (21 November 1991).
2752:
2203:into 100 times heavier constituents of
2157:symmetry-breaking generically produces
1494:obey symmetries, but the lowest-energy
1162:
51:
2970:Journal of Physics: Conference Series
2561:of a crystal, or continuous (e.g., a
2358:dynamical breaking of chiral symmetry
7:
3778:
3027:. Knopf Doubleday Publishing Group.
1880:
1772:
1647:
1368:Grand potential / Landau free energy
2492:Generalisation and technical usage
1681:
1668:
1482:, by which a physical system in a
25:
3280:"The Nobel Prize in Physics 2008"
3021:Steven Weinberg (20 April 2011).
2726:1964 PRL symmetry breaking papers
2583:Royal Swedish Academy of Sciences
4572:
4571:
3777:
3766:
3765:
3510:
2849:. New York: BasicBooks. p.
2766:. World Scientific. p. 15.
2125:symmetry breaking (SSB) because
2391:fractional quantum Hall liquids
4521:Relativistic quantum mechanics
3693:Causal dynamical triangulation
3000:10.1088/1742-6596/626/1/012001
2760:Miransky, Vladimir A. (1993).
2516:member is distinct, only that
1836:
1827:
1813:
1804:
1791:
1785:
1753:
1747:
1705:
1699:
1600:
1594:
1542:fractional quantum Hall effect
1:
4499:Quantum statistical mechanics
4276:Quantum differential calculus
4198:Delayed-choice quantum eraser
3981:Symmetry in quantum mechanics
3532:Spontaneous symmetry breaking
3314:Spontaneous symmetry breaking
3249:10.1103/PhysRevLett.99.030602
2790:Patterns of Symmetry Breaking
2705:Second-order phase transition
1977:In fact, any other choice of
1737:It is in this potential term
1472:Spontaneous symmetry breaking
188:Spontaneous symmetry breaking
148:Symmetry in quantum mechanics
18:Spontaneously broken symmetry
3158:Chen, Xie; Gu, Zheng-Cheng;
2356:, which is connected to the
2149:, depending on the relevant
2050:Consider a uniform layer of
4301:Quantum stochastic calculus
4291:Quantum measurement problem
4213:MachâZehnder interferometer
2913:American Journal of Physics
2841:Edelman, Gerald M. (1992).
2691:of chiral symmetry breaking
2373:In condensed matter physics
2311:Dynamical symmetry breaking
2275:electromagnetic interaction
1210:Indistinguishable particles
4639:
3194:10.1103/physrevb.82.155138
3080:10.1103/PhysRevD.68.103514
2222:
2172:
2133:, such as two-dimensional
1563:ColemanâWeinberg potential
1560:
1531:explicit symmetry breaking
183:Explicit symmetry breaking
4567:
4361:Quantum complexity theory
4339:Quantum cellular automata
4044:Path integral formulation
3761:
3698:Canonical quantum gravity
3508:
2793:. Springer. p. 141.
1878:(vacuum states) given by
1498:do not exhibit that same
339:BargmannâWigner equations
37:: At high energy levels (
4428:Quantum machine learning
4408:Quantum key distribution
4398:Quantum image processing
4388:Quantum error correction
4238:Wheeler's delayed choice
3703:Superfluid vacuum theory
3137:10.1103/PhysRevD.41.1647
2654:Gauge gravitation theory
2639:Chiral symmetry breaking
2599:chiral symmetry breaking
2581:On October 7, 2008, the
2337:electroweak interactions
2175:Chiral symmetry breaking
1759:{\displaystyle V(\phi )}
1606:{\displaystyle V(\phi )}
1523:translational symmetry.
4344:Quantum finite automata
3485:Quantum electrodynamics
3475:Electroweak interaction
3218:Physical Review Letters
2964:Kibble, T W B. (2015).
2679:Higgs field (classical)
2076:gravitational potential
2022:FRW cosmological models
1253:Thermodynamic ensembles
1205:Spinâstatistics theorem
364:Electroweak interaction
359:Quantum electrodynamics
334:WheelerâDeWitt equation
221:Background field method
4613:Quantum chromodynamics
4448:Quantum neural network
3463:Quantum chromodynamics
3278:The Nobel Foundation.
2864:Goldstone, J. (1961).
2587:Nobel Prize in Physics
2362:quantum chromodynamics
2209:NambuâGoldstone bosons
2189:quantum chromodynamics
2087:two-balloon experiment
1928:
1851:
1760:
1715:
1639:
1614:
1607:
1580:Graph of Goldstone's "
369:Quantum chromodynamics
246:Effective field theory
46:
4473:Quantum teleportation
4001:Waveâparticle duality
3579:Cosmological constant
2695:MerminâWagner theorem
2595:University of Chicago
2279:WeinbergâSalam theory
2045:NambuâGoldstone boson
1983:NambuâGoldstone boson
1929:
1852:
1761:
1716:
1640:
1638:{\displaystyle \phi }
1608:
1584:" potential function
1579:
1358:Helmholtz free energy
1287:Isoenthalpicâisobaric
1164:Statistical mechanics
324:KleinâGordon equation
266:LSZ reduction formula
33:
4603:Quantum field theory
4504:Quantum field theory
4433:Quantum metamaterial
4378:Quantum cryptography
4108:Consistent histories
3688:Loop quantum gravity
3627:Theory of everything
3622:Grand Unified Theory
3596:Neutrino oscillation
3443:Quantum field theory
2721:Tachyon condensation
2664:Grand unified theory
2548:NambuâGoldstone mode
2350:fermionic condensate
2300:, detected in 2012.
2193:quantum field theory
1887:
1779:
1741:
1654:
1629:
1588:
407:Theory of everything
261:Lattice field theory
231:Correlation function
53:Quantum field theory
4598:Theoretical physics
4489:Quantum fluctuation
4458:Quantum programming
4418:Quantum logic gates
4403:Quantum information
4383:Quantum electronics
3858:Classical mechanics
3655:Split supersymmetry
3617:KaluzaâKlein theory
3490:Fermi's interaction
3241:2007PhRvL..99c0602K
3186:2010PhRvB..82o5138C
3129:1990PhRvD..41.1647B
3107:Christopher T. Hill
3072:2003PhRvD..68j3514J
2992:2015JPhCS.626a2001K
2935:2012AmJPh..80..891M
2882:1961NCim...19..154G
2401:Continuous symmetry
2380:rotational symmetry
2185:strong interactions
2141:, zero-dimensional
2131:topological defects
2095:In particle physics
2068:rotational velocity
1966:. This state has a
1619:scalar field theory
1570:spontaneously break
1488:equations of motion
1476:spontaneous process
1295:Isothermalâisobaric
1198:Particle statistics
386:Incomplete theories
4542:in popular culture
4324:Quantum algorithms
4172:Von NeumannâWigner
4152:Objective collapse
3863:Old quantum theory
3683:Superstring theory
3453:Strong interaction
3103:William A. Bardeen
2890:10.1007/BF02812722
2689:Magnetic catalysis
2634:Catastrophe theory
2229:Yukawa interaction
2207:. The approximate
2137:, one-dimensional
2113:by the same amount
1924:
1847:
1756:
1711:
1635:
1625:of a scalar field
1615:
1603:
1557:Sombrero potential
1235:Anyonic statistics
271:Partition function
198:Topological charge
118:General relativity
113:Special relativity
47:
4585:
4584:
4559:Quantum mysticism
4537:Schrödinger's cat
4468:Quantum simulator
4438:Quantum metrology
4366:Quantum computing
4329:Quantum amplifier
4306:Quantum spacetime
4271:Quantum cosmology
4261:Quantum chemistry
3976:Scattering theory
3924:Zero-point energy
3919:Degenerate levels
3827:Quantum mechanics
3793:
3792:
3716:
3715:
3591:Strong CP problem
3569:Hierarchy problem
3116:Physical Review D
3050:Physical Review D
3034:978-0-307-78786-6
2943:10.1119/1.4739927
2716:Symmetry breaking
2615:explicit breaking
2607:Toshihide Maskawa
2585:awarded the 2008
2532:expectation value
2475:Coulomb potential
2422:Curie temperature
2407:Curie temperature
2366:superconductivity
2304:Superconductivity
2247:Elitzur's theorem
2243:superconductivity
2072:equilibrium point
2004:Curie temperature
1949:
1948:
1909:
1872:
1871:
1768:Jeffrey Goldstone
1735:
1734:
1538:phase transitions
1512:quantum mechanics
1480:symmetry breaking
1469:
1468:
1363:Gibbs free energy
1215:MaxwellâBoltzmann
1158:
1157:
251:Expectation value
226:BRST quantization
173:Poincaré symmetry
128:YangâMills theory
108:Quantum mechanics
16:(Redirected from
4630:
4575:
4574:
4286:Quantum geometry
4281:Quantum dynamics
4138:Superdeterminism
4034:Matrix mechanics
3889:Braâket notation
3820:
3813:
3806:
3797:
3781:
3780:
3769:
3768:
3559:
3514:
3513:
3495:Weak hypercharge
3480:Weak interaction
3421:Particle physics
3400:
3393:
3386:
3377:
3295:
3294:
3292:
3290:
3275:
3269:
3268:
3234:
3212:
3206:
3205:
3179:
3155:
3149:
3148:
3123:(5): 1647â1660.
3099:
3093:
3090:
3084:
3083:
3065:
3045:
3039:
3038:
3018:
3012:
3011:
2985:
2961:
2955:
2954:
2928:
2908:
2902:
2901:
2870:Il Nuovo Cimento
2861:
2855:
2854:
2848:
2838:
2832:
2831:
2811:
2805:
2804:
2784:
2778:
2777:
2757:
2741:
2611:Kyoto University
2603:Makoto Kobayashi
2552:Goldstone bosons
2479:Yukawa potential
2457:
2450:
2415:
2354:quark condensate
2326:effective action
2267:weak interaction
2260:
2252:gauge symmetries
2235:gauge symmetries
2163:cosmic inflation
2101:particle physics
2057:convection cells
1965:
1943:
1933:
1931:
1930:
1925:
1923:
1922:
1910:
1905:
1897:
1881:
1866:
1856:
1854:
1853:
1848:
1845:
1844:
1839:
1830:
1822:
1821:
1816:
1807:
1773:
1765:
1763:
1762:
1757:
1729:
1720:
1718:
1717:
1712:
1689:
1688:
1676:
1675:
1663:
1662:
1648:
1644:
1642:
1641:
1636:
1612:
1610:
1609:
1604:
1496:vacuum solutions
1461:
1454:
1447:
1240:Braid statistics
1174:
1160:
1150:
1143:
1136:
241:Effective action
168:Lorentz symmetry
93:Electromagnetism
63:
49:
21:
4638:
4637:
4633:
4632:
4631:
4629:
4628:
4627:
4588:
4587:
4586:
4581:
4563:
4549:Wigner's friend
4525:
4516:Quantum gravity
4477:
4463:Quantum sensing
4443:Quantum network
4423:Quantum machine
4393:Quantum imaging
4356:Quantum circuit
4351:Quantum channel
4310:
4256:Quantum biology
4242:
4218:ElitzurâVaidman
4193:DavissonâGermer
4176:
4128:Hidden-variable
4118:de BroglieâBohm
4095:Interpretations
4089:
4053:
4007:
3894:Complementarity
3872:
3829:
3824:
3794:
3789:
3757:
3712:
3670:Quantum gravity
3664:
3631:
3600:
3553:
3546:
3537:Higgs mechanism
3515:
3511:
3506:
3409:
3404:
3304:
3299:
3298:
3288:
3286:
3277:
3276:
3272:
3214:
3213:
3209:
3157:
3156:
3152:
3111:Manfred Lindner
3101:
3100:
3096:
3091:
3087:
3047:
3046:
3042:
3035:
3020:
3019:
3015:
2963:
2962:
2958:
2919:(10): 891â897.
2910:
2909:
2905:
2863:
2862:
2858:
2840:
2839:
2835:
2828:
2813:
2812:
2808:
2801:
2786:
2785:
2781:
2774:
2759:
2758:
2754:
2749:
2738:
2735:
2730:
2684:Irreversibility
2669:Higgs mechanism
2659:Goldstone boson
2624:
2579:
2525:order parameter
2503:Goldstone boson
2494:
2452:
2433:
2410:
2403:
2384:liquid crystals
2375:
2364:. Conventional
2341:Higgs mechanism
2313:
2294:Higgs mechanism
2258:
2239:Higgs mechanism
2231:
2225:Higgs mechanism
2223:Main articles:
2221:
2219:Higgs mechanism
2181:chiral symmetry
2177:
2171:
2169:Chiral symmetry
2097:
2037:superconductors
2011:Euclidean group
1991:
1960:
1955:between 0 and 2
1941:
1911:
1885:
1884:
1864:
1834:
1811:
1777:
1776:
1739:
1738:
1727:
1680:
1667:
1652:
1651:
1627:
1626:
1621:. The relevant
1586:
1585:
1565:
1559:
1554:
1529:Conversely, in
1508:
1465:
1436:
1435:
1381:
1373:
1372:
1348:Internal energy
1343:
1333:
1332:
1308:
1300:
1299:
1279:Grand canonical
1255:
1245:
1244:
1200:
1154:
1125:
1124:
1123:
1121:
425:
417:
416:
412:Quantum gravity
387:
379:
378:
374:Higgs mechanism
354:
344:
343:
329:Proca equations
314:
306:
305:
291:Renormalization
256:Feynman diagram
211:
203:
202:
143:
133:
132:
83:
68:
66:Feynman diagram
28:
23:
22:
15:
12:
11:
5:
4636:
4634:
4626:
4625:
4623:Quantum phases
4620:
4615:
4610:
4608:Standard Model
4605:
4600:
4590:
4589:
4583:
4582:
4580:
4579:
4568:
4565:
4564:
4562:
4561:
4556:
4551:
4546:
4545:
4544:
4533:
4531:
4527:
4526:
4524:
4523:
4518:
4513:
4512:
4511:
4501:
4496:
4494:Casimir effect
4491:
4485:
4483:
4479:
4478:
4476:
4475:
4470:
4465:
4460:
4455:
4453:Quantum optics
4450:
4445:
4440:
4435:
4430:
4425:
4420:
4415:
4410:
4405:
4400:
4395:
4390:
4385:
4380:
4375:
4374:
4373:
4363:
4358:
4353:
4348:
4347:
4346:
4336:
4331:
4326:
4320:
4318:
4312:
4311:
4309:
4308:
4303:
4298:
4293:
4288:
4283:
4278:
4273:
4268:
4263:
4258:
4252:
4250:
4244:
4243:
4241:
4240:
4235:
4230:
4228:Quantum eraser
4225:
4220:
4215:
4210:
4205:
4200:
4195:
4190:
4184:
4182:
4178:
4177:
4175:
4174:
4169:
4164:
4159:
4154:
4149:
4144:
4143:
4142:
4141:
4140:
4125:
4120:
4115:
4110:
4105:
4099:
4097:
4091:
4090:
4088:
4087:
4082:
4077:
4072:
4067:
4061:
4059:
4055:
4054:
4052:
4051:
4046:
4041:
4036:
4031:
4026:
4021:
4015:
4013:
4009:
4008:
4006:
4005:
4004:
4003:
3998:
3988:
3983:
3978:
3973:
3968:
3963:
3958:
3953:
3948:
3943:
3938:
3933:
3928:
3927:
3926:
3921:
3916:
3911:
3901:
3899:Density matrix
3896:
3891:
3886:
3880:
3878:
3874:
3873:
3871:
3870:
3865:
3860:
3855:
3854:
3853:
3843:
3837:
3835:
3831:
3830:
3825:
3823:
3822:
3815:
3808:
3800:
3791:
3790:
3788:
3787:
3775:
3762:
3759:
3758:
3756:
3755:
3750:
3745:
3740:
3735:
3730:
3724:
3722:
3718:
3717:
3714:
3713:
3711:
3710:
3708:Twistor theory
3705:
3700:
3695:
3690:
3685:
3680:
3674:
3672:
3666:
3665:
3663:
3662:
3657:
3652:
3647:
3641:
3639:
3633:
3632:
3630:
3629:
3624:
3619:
3614:
3608:
3606:
3602:
3601:
3599:
3598:
3593:
3588:
3587:
3586:
3576:
3571:
3565:
3563:
3556:
3554:Standard Model
3548:
3547:
3545:
3544:
3539:
3534:
3529:
3523:
3521:
3517:
3516:
3509:
3507:
3505:
3504:
3503:
3502:
3497:
3492:
3487:
3482:
3472:
3471:
3470:
3465:
3460:
3450:
3445:
3440:
3439:
3438:
3433:
3428:
3417:
3415:
3411:
3410:
3407:Standard Model
3405:
3403:
3402:
3395:
3388:
3380:
3374:
3373:
3368:
3363:
3358:
3346:
3341:
3336:
3331:
3326:
3321:
3316:
3311:
3303:
3302:External links
3300:
3297:
3296:
3284:nobelprize.org
3270:
3207:
3170:(15): 155138.
3160:Wen, Xiao-Gang
3150:
3094:
3085:
3063:hep-ph/0308134
3056:(10): 103514.
3040:
3033:
3013:
2956:
2903:
2876:(1): 154â164.
2856:
2833:
2826:
2806:
2799:
2779:
2772:
2751:
2750:
2748:
2745:
2744:
2743:
2734:
2731:
2729:
2728:
2723:
2718:
2713:
2707:
2702:
2697:
2692:
2686:
2681:
2676:
2671:
2666:
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2625:
2623:
2620:
2591:Yoichiro Nambu
2578:
2575:
2571:quantum theory
2510:symmetry group
2493:
2490:
2402:
2399:
2374:
2371:
2345:standard model
2333:Higgs particle
2312:
2309:
2290:W and Z bosons
2286:Standard Model
2263:W and Z bosons
2220:
2217:
2173:Main article:
2170:
2167:
2151:homotopy group
2139:cosmic strings
2109:gauge symmetry
2096:
2093:
2092:
2091:
2083:
2060:
2048:
2040:
2033:
2025:
2018:
2007:
1990:
1989:Other examples
1987:
1947:
1946:
1937:
1935:
1921:
1918:
1914:
1908:
1904:
1900:
1895:
1892:
1870:
1869:
1860:
1858:
1843:
1838:
1833:
1829:
1825:
1820:
1815:
1810:
1806:
1802:
1799:
1796:
1793:
1790:
1787:
1784:
1755:
1752:
1749:
1746:
1733:
1732:
1723:
1721:
1710:
1707:
1704:
1701:
1698:
1695:
1692:
1687:
1683:
1679:
1674:
1670:
1666:
1661:
1634:
1602:
1599:
1596:
1593:
1558:
1555:
1553:
1550:
1507:
1504:
1467:
1466:
1464:
1463:
1456:
1449:
1441:
1438:
1437:
1434:
1433:
1428:
1423:
1418:
1413:
1408:
1403:
1398:
1393:
1388:
1382:
1379:
1378:
1375:
1374:
1371:
1370:
1365:
1360:
1355:
1350:
1344:
1339:
1338:
1335:
1334:
1331:
1330:
1325:
1320:
1315:
1309:
1306:
1305:
1302:
1301:
1298:
1297:
1289:
1281:
1273:
1265:
1263:Microcanonical
1256:
1251:
1250:
1247:
1246:
1243:
1242:
1237:
1232:
1230:Parastatistics
1227:
1222:
1217:
1212:
1207:
1201:
1196:
1195:
1192:
1191:
1190:
1189:
1187:Kinetic theory
1184:
1182:Thermodynamics
1176:
1175:
1167:
1166:
1156:
1155:
1153:
1152:
1145:
1138:
1130:
1127:
1126:
1119:
1118:
1113:
1108:
1103:
1098:
1093:
1088:
1083:
1078:
1073:
1068:
1063:
1058:
1053:
1048:
1043:
1038:
1033:
1028:
1023:
1018:
1013:
1008:
1003:
998:
993:
988:
983:
978:
973:
968:
963:
958:
953:
948:
943:
938:
933:
928:
923:
918:
913:
908:
903:
898:
893:
888:
883:
878:
873:
868:
863:
858:
853:
848:
843:
838:
833:
828:
823:
818:
813:
808:
803:
798:
793:
788:
783:
778:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
628:
623:
618:
613:
608:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
478:
473:
468:
463:
458:
453:
448:
443:
438:
433:
427:
426:
423:
422:
419:
418:
415:
414:
409:
404:
399:
394:
388:
385:
384:
381:
380:
377:
376:
371:
366:
361:
355:
352:Standard Model
350:
349:
346:
345:
342:
341:
336:
331:
326:
321:
319:Dirac equation
315:
312:
311:
308:
307:
304:
303:
301:Wick's theorem
298:
293:
288:
286:Regularization
283:
278:
273:
268:
263:
258:
253:
248:
243:
238:
233:
228:
223:
218:
212:
209:
208:
205:
204:
201:
200:
195:
193:Noether charge
190:
185:
180:
178:Gauge symmetry
175:
170:
165:
160:
155:
150:
144:
139:
138:
135:
134:
131:
130:
125:
120:
115:
110:
105:
100:
95:
90:
84:
81:
80:
77:
76:
70:
69:
64:
56:
55:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4635:
4624:
4621:
4619:
4616:
4614:
4611:
4609:
4606:
4604:
4601:
4599:
4596:
4595:
4593:
4578:
4570:
4569:
4566:
4560:
4557:
4555:
4552:
4550:
4547:
4543:
4540:
4539:
4538:
4535:
4534:
4532:
4528:
4522:
4519:
4517:
4514:
4510:
4507:
4506:
4505:
4502:
4500:
4497:
4495:
4492:
4490:
4487:
4486:
4484:
4480:
4474:
4471:
4469:
4466:
4464:
4461:
4459:
4456:
4454:
4451:
4449:
4446:
4444:
4441:
4439:
4436:
4434:
4431:
4429:
4426:
4424:
4421:
4419:
4416:
4414:
4413:Quantum logic
4411:
4409:
4406:
4404:
4401:
4399:
4396:
4394:
4391:
4389:
4386:
4384:
4381:
4379:
4376:
4372:
4369:
4368:
4367:
4364:
4362:
4359:
4357:
4354:
4352:
4349:
4345:
4342:
4341:
4340:
4337:
4335:
4332:
4330:
4327:
4325:
4322:
4321:
4319:
4317:
4313:
4307:
4304:
4302:
4299:
4297:
4294:
4292:
4289:
4287:
4284:
4282:
4279:
4277:
4274:
4272:
4269:
4267:
4266:Quantum chaos
4264:
4262:
4259:
4257:
4254:
4253:
4251:
4249:
4245:
4239:
4236:
4234:
4233:SternâGerlach
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4185:
4183:
4179:
4173:
4170:
4168:
4167:Transactional
4165:
4163:
4160:
4158:
4157:Quantum logic
4155:
4153:
4150:
4148:
4145:
4139:
4136:
4135:
4134:
4131:
4130:
4129:
4126:
4124:
4121:
4119:
4116:
4114:
4111:
4109:
4106:
4104:
4101:
4100:
4098:
4096:
4092:
4086:
4083:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4062:
4060:
4056:
4050:
4047:
4045:
4042:
4040:
4037:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4016:
4014:
4010:
4002:
3999:
3997:
3994:
3993:
3992:
3991:Wave function
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3966:Superposition
3964:
3962:
3961:Quantum state
3959:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3932:
3929:
3925:
3922:
3920:
3917:
3915:
3914:Excited state
3912:
3910:
3907:
3906:
3905:
3902:
3900:
3897:
3895:
3892:
3890:
3887:
3885:
3882:
3881:
3879:
3875:
3869:
3866:
3864:
3861:
3859:
3856:
3852:
3849:
3848:
3847:
3844:
3842:
3839:
3838:
3836:
3832:
3828:
3821:
3816:
3814:
3809:
3807:
3802:
3801:
3798:
3786:
3785:
3776:
3774:
3773:
3764:
3763:
3760:
3754:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3734:
3731:
3729:
3726:
3725:
3723:
3719:
3709:
3706:
3704:
3701:
3699:
3696:
3694:
3691:
3689:
3686:
3684:
3681:
3679:
3678:String theory
3676:
3675:
3673:
3671:
3667:
3661:
3658:
3656:
3653:
3651:
3648:
3646:
3643:
3642:
3640:
3638:
3637:Supersymmetry
3634:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3609:
3607:
3603:
3597:
3594:
3592:
3589:
3585:
3582:
3581:
3580:
3577:
3575:
3572:
3570:
3567:
3566:
3564:
3560:
3557:
3555:
3549:
3543:
3540:
3538:
3535:
3533:
3530:
3528:
3525:
3524:
3522:
3518:
3501:
3498:
3496:
3493:
3491:
3488:
3486:
3483:
3481:
3478:
3477:
3476:
3473:
3469:
3466:
3464:
3461:
3459:
3456:
3455:
3454:
3451:
3449:
3446:
3444:
3441:
3437:
3434:
3432:
3429:
3427:
3424:
3423:
3422:
3419:
3418:
3416:
3412:
3408:
3401:
3396:
3394:
3389:
3387:
3382:
3381:
3378:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3356:0-470-17057-3
3353:
3350:
3347:
3345:
3342:
3340:
3337:
3335:
3332:
3330:
3327:
3325:
3322:
3320:
3317:
3315:
3312:
3310:
3306:
3305:
3301:
3285:
3281:
3274:
3271:
3266:
3262:
3258:
3254:
3250:
3246:
3242:
3238:
3233:
3228:
3225:(3): 030602.
3224:
3220:
3219:
3211:
3208:
3203:
3199:
3195:
3191:
3187:
3183:
3178:
3173:
3169:
3165:
3161:
3154:
3151:
3146:
3142:
3138:
3134:
3130:
3126:
3122:
3118:
3117:
3112:
3108:
3104:
3098:
3095:
3089:
3086:
3081:
3077:
3073:
3069:
3064:
3059:
3055:
3051:
3044:
3041:
3036:
3030:
3026:
3025:
3017:
3014:
3009:
3005:
3001:
2997:
2993:
2989:
2984:
2979:
2976:(1): 012001.
2975:
2971:
2967:
2960:
2957:
2952:
2948:
2944:
2940:
2936:
2932:
2927:
2922:
2918:
2914:
2907:
2904:
2899:
2895:
2891:
2887:
2883:
2879:
2875:
2871:
2867:
2860:
2857:
2852:
2847:
2846:
2837:
2834:
2829:
2827:9780521426732
2823:
2819:
2818:
2810:
2807:
2802:
2800:9781402017452
2796:
2792:
2791:
2783:
2780:
2775:
2769:
2765:
2764:
2756:
2753:
2746:
2740:
2737:
2736:
2732:
2727:
2724:
2722:
2719:
2717:
2714:
2711:
2708:
2706:
2703:
2701:
2700:Norton's dome
2698:
2696:
2693:
2690:
2687:
2685:
2682:
2680:
2677:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2626:
2621:
2619:
2616:
2612:
2608:
2604:
2601:. Physicists
2600:
2596:
2592:
2588:
2584:
2576:
2574:
2572:
2568:
2564:
2560:
2555:
2553:
2549:
2545:
2541:
2537:
2536:ordered phase
2533:
2531:
2526:
2521:
2519:
2515:
2511:
2506:
2504:
2499:
2491:
2489:
2487:
2484:
2480:
2476:
2471:
2467:
2463:
2459:
2455:
2448:
2444:
2440:
2436:
2431:
2427:
2423:
2419:
2413:
2408:
2400:
2398:
2396:
2392:
2387:
2385:
2381:
2372:
2370:
2367:
2363:
2359:
2355:
2351:
2346:
2342:
2338:
2334:
2329:
2327:
2321:
2319:
2310:
2308:
2305:
2301:
2299:
2295:
2291:
2287:
2282:
2280:
2276:
2273:mediates the
2272:
2268:
2264:
2255:
2253:
2248:
2244:
2240:
2236:
2230:
2226:
2218:
2216:
2214:
2210:
2206:
2202:
2198:
2194:
2190:
2186:
2182:
2176:
2168:
2166:
2164:
2160:
2156:
2152:
2148:
2144:
2140:
2136:
2132:
2128:
2124:
2123:
2116:
2114:
2110:
2106:
2105:force carrier
2102:
2094:
2088:
2084:
2081:
2077:
2073:
2069:
2065:
2061:
2058:
2053:
2049:
2046:
2041:
2038:
2034:
2030:
2026:
2023:
2019:
2016:
2012:
2008:
2005:
2001:
2000:magnetization
1997:
1996:ferromagnetic
1993:
1992:
1988:
1986:
1984:
1980:
1975:
1973:
1969:
1963:
1958:
1954:
1951:for any real
1945:
1938:
1936:
1919:
1916:
1912:
1906:
1902:
1898:
1893:
1890:
1883:
1882:
1879:
1877:
1868:
1861:
1859:
1841:
1831:
1823:
1818:
1808:
1800:
1797:
1794:
1788:
1782:
1775:
1774:
1771:
1769:
1750:
1744:
1731:
1724:
1722:
1708:
1702:
1696:
1693:
1690:
1685:
1677:
1672:
1664:
1650:
1649:
1646:
1632:
1624:
1620:
1597:
1591:
1583:
1578:
1574:
1571:
1564:
1556:
1551:
1549:
1545:
1543:
1539:
1534:
1532:
1527:
1524:
1521:
1517:
1513:
1505:
1503:
1501:
1497:
1493:
1489:
1485:
1481:
1477:
1473:
1462:
1457:
1455:
1450:
1448:
1443:
1442:
1440:
1439:
1432:
1429:
1427:
1424:
1422:
1419:
1417:
1414:
1412:
1409:
1407:
1404:
1402:
1399:
1397:
1394:
1392:
1389:
1387:
1384:
1383:
1377:
1376:
1369:
1366:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1345:
1342:
1337:
1336:
1329:
1326:
1324:
1321:
1319:
1316:
1314:
1311:
1310:
1304:
1303:
1296:
1293:
1290:
1288:
1285:
1282:
1280:
1277:
1274:
1272:
1269:
1266:
1264:
1261:
1258:
1257:
1254:
1249:
1248:
1241:
1238:
1236:
1233:
1231:
1228:
1226:
1223:
1221:
1220:BoseâEinstein
1218:
1216:
1213:
1211:
1208:
1206:
1203:
1202:
1199:
1194:
1193:
1188:
1185:
1183:
1180:
1179:
1178:
1177:
1173:
1169:
1168:
1165:
1161:
1151:
1146:
1144:
1139:
1137:
1132:
1131:
1129:
1128:
1122:
1117:
1114:
1112:
1109:
1107:
1104:
1102:
1099:
1097:
1094:
1092:
1091:Zamolodchikov
1089:
1087:
1086:Zamolodchikov
1084:
1082:
1079:
1077:
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1014:
1012:
1009:
1007:
1004:
1002:
999:
997:
994:
992:
989:
987:
984:
982:
979:
977:
974:
972:
969:
967:
964:
962:
959:
957:
954:
952:
949:
947:
944:
942:
939:
937:
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
862:
859:
857:
854:
852:
849:
847:
844:
842:
839:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
617:
614:
612:
609:
607:
604:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
574:
572:
569:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
467:
464:
462:
459:
457:
454:
452:
449:
447:
444:
442:
439:
437:
434:
432:
429:
428:
421:
420:
413:
410:
408:
405:
403:
400:
398:
397:Supersymmetry
395:
393:
392:String theory
390:
389:
383:
382:
375:
372:
370:
367:
365:
362:
360:
357:
356:
353:
348:
347:
340:
337:
335:
332:
330:
327:
325:
322:
320:
317:
316:
310:
309:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
272:
269:
267:
264:
262:
259:
257:
254:
252:
249:
247:
244:
242:
239:
237:
234:
232:
229:
227:
224:
222:
219:
217:
214:
213:
207:
206:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
174:
171:
169:
166:
164:
161:
159:
156:
154:
151:
149:
146:
145:
142:
137:
136:
129:
126:
124:
121:
119:
116:
114:
111:
109:
106:
104:
101:
99:
96:
94:
91:
89:
86:
85:
79:
78:
75:
72:
71:
67:
62:
58:
57:
54:
50:
44:
40:
36:
32:
19:
4296:Quantum mind
4208:FranckâHertz
4070:KleinâGordon
4019:Formulations
4012:Formulations
3941:Interference
3931:Entanglement
3909:Ground state
3904:Energy level
3877:Fundamentals
3841:Introduction
3782:
3770:
3660:Supergravity
3531:
3520:Constituents
3500:Weak isospin
3458:Color charge
3448:Gauge theory
3287:. Retrieved
3283:
3273:
3222:
3216:
3210:
3167:
3164:Phys. Rev. B
3163:
3153:
3120:
3114:
3097:
3088:
3053:
3049:
3043:
3023:
3016:
2973:
2969:
2959:
2916:
2912:
2906:
2873:
2869:
2859:
2844:
2836:
2816:
2809:
2789:
2782:
2762:
2755:
2739:
2712:in chemistry
2644:CP-violation
2580:
2569:of the full
2567:vacuum state
2556:
2547:
2543:
2540:vacuum state
2529:
2522:
2517:
2513:
2507:
2495:
2483:mirror plane
2472:
2468:
2464:
2460:
2453:
2446:
2442:
2438:
2434:
2432:) such that
2429:
2425:
2417:
2411:
2404:
2395:spin-liquids
2388:
2376:
2352:â e.g., the
2330:
2322:
2314:
2302:
2283:
2269:, while the
2259:SU(2) Ă U(1)
2256:
2251:
2232:
2178:
2135:domain walls
2126:
2121:
2117:
2112:
2098:
1978:
1976:
1971:
1961:
1956:
1952:
1950:
1939:
1873:
1862:
1736:
1725:
1616:
1569:
1566:
1546:
1535:
1528:
1525:
1514:) which are
1509:
1471:
1470:
1291:
1283:
1275:
1267:
1259:
1120:
966:Stueckelberg
706:Jona-Lasinio
296:Vacuum state
281:Quantization
187:
123:Gauge theory
103:Strong force
88:Field theory
42:
38:
34:
4554:EPR paradox
4334:Quantum bus
4203:Double-slit
4181:Experiments
4147:Many-worlds
4085:Schrödinger
4049:Phase space
4039:Schrödinger
4029:Interaction
3986:Uncertainty
3956:Nonlocality
3951:Measurement
3946:Decoherence
3936:Hamiltonian
3721:Experiments
3612:Technicolor
3574:Dark matter
3468:Quark model
3436:Higgs boson
3431:Gauge boson
3289:January 15,
2674:Higgs boson
2577:Nobel Prize
2559:space group
2544:Wigner mode
2298:Higgs boson
2122:spontaneous
2080:equidistant
2029:electroweak
2015:space group
1416:von Neumann
1225:FermiâDirac
1106:Zinn-Justin
956:Sommerfield
881:Pomeranchuk
851:Osterwalder
846:Oppenheimer
776:ĆopuszaĆski
601:Fredenhagen
402:Technicolor
4592:Categories
4482:Extensions
4316:Technology
4162:Relational
4113:Copenhagen
4024:Heisenberg
3971:Tunnelling
3834:Background
3728:Gran Sasso
3552:Beyond the
3527:CKM matrix
3414:Background
2983:1502.06276
2773:9810215584
2747:References
2649:Fermi ball
2318:Lagrangian
1623:Lagrangian
1561:See also:
1492:Lagrangian
1380:Scientists
1341:Potentials
1101:Zimmermann
996:Vainshtein
741:Kontsevich
686:Iliopoulos
661:Heisenberg
486:Bogoliubov
424:Scientists
276:Propagator
163:T-symmetry
158:P-symmetry
153:C-symmetry
141:Symmetries
98:Weak force
82:Background
4188:Bell test
4058:Equations
3884:Born rule
3232:0704.3435
3177:1004.3835
3008:119290021
2951:119131875
2926:1205.4773
2898:120409034
2593:, of the
2563:Lie group
2498:symmetric
2159:monopoles
2145:, and/or
2143:monopoles
2066:. As the
1920:θ
1891:ϕ
1832:ϕ
1809:ϕ
1798:−
1789:ϕ
1751:ϕ
1703:ϕ
1694:−
1691:ϕ
1686:μ
1682:∂
1678:ϕ
1673:μ
1669:∂
1633:ϕ
1598:ϕ
1516:invariant
1484:symmetric
1411:Ehrenfest
1391:Boltzmann
1271:Canonical
1036:Wetterich
1021:Weisskopf
971:Sudarshan
921:Schwinger
836:Nishijima
801:Maldacena
766:Leutwyler
731:Kinoshita
631:Goldstone
621:Gell-Mann
536:Doplicher
313:Equations
4618:Symmetry
4577:Category
4371:Timeline
4123:Ensemble
4103:Bayesian
3996:Collapse
3868:Glossary
3851:Timeline
3772:Category
3753:Tevatron
3605:Theories
3562:Evidence
3426:Fermions
3265:37983980
3257:17678276
3202:14593420
3145:10012522
2622:See also
2486:symmetry
2416:, where
2197:nucleons
2147:textures
2064:diameter
2027:For the
1582:sombrero
1552:Examples
1520:symmetry
1518:under a
1506:Overview
1500:symmetry
1406:Einstein
1353:Enthalpy
1318:Einstein
1051:Wightman
1016:Weinberg
1006:Virasoro
986:Tomonaga
981:Thirring
976:Symanzik
936:Semenoff
911:Schrader
876:Polyakov
796:Majorana
736:Klebanov
691:Ivanenko
681:'t Hooft
651:Guralnik
596:Fröhlich
591:Fritzsch
586:Frampton
501:Buchholz
446:Bargmann
436:Anderson
236:Crossing
4530:Related
4509:History
4248:Science
4080:Rydberg
3846:History
3784:Commons
3748:Super-K
3584:problem
3237:Bibcode
3182:Bibcode
3125:Bibcode
3068:Bibcode
2988:Bibcode
2931:Bibcode
2878:Bibcode
2554:arise.
2409:and at
2343:in the
2205:baryons
2183:of the
2127:nothing
1490:or the
1386:Maxwell
1061:Wilczek
1026:Wentzel
1001:Veltman
946:Shirkov
941:Shifman
931:Seiberg
916:Schwarz
896:Rubakov
821:Naimark
771:Lipatov
761:Lehmann
726:Kendall
616:Gelfand
611:Glashow
571:Feynman
551:Faddeev
546:Englert
516:Coleman
506:Cachazo
491:Brodsky
476:Bjorken
466:Berezin
456:Belavin
216:Anomaly
74:History
4223:Popper
3354:
3263:
3255:
3200:
3143:
3031:
3006:
2949:
2896:
2824:
2797:
2770:
2530:vacuum
2518:one is
2393:, and
2271:photon
2201:quarks
2191:, the
2103:, the
2090:state.
1876:minima
1421:Tolman
1307:Models
1116:Zumino
1081:Yukawa
1071:Witten
1066:Wilson
1056:Wigner
991:Tyutin
951:Skyrme
901:Ruelle
871:Plefka
866:Peskin
856:Parisi
816:MĂžller
806:Migdal
791:Maiani
786:LĂŒders
751:Landau
746:Kuraev
721:KÀllén
711:Jordan
696:Jackiw
636:Gribov
526:DeWitt
521:Dashen
511:Callan
481:Bleuer
451:Becchi
441:Anselm
4133:Local
4075:Pauli
4065:Dirac
3650:NMSSM
3261:S2CID
3227:arXiv
3198:S2CID
3172:arXiv
3058:arXiv
3004:S2CID
2978:arXiv
2947:S2CID
2921:arXiv
2894:S2CID
2733:Notes
2609:, of
2514:which
2441:) = â
2213:pions
2052:fluid
1474:is a
1431:Fermi
1426:Debye
1401:Gibbs
1328:Potts
1323:Ising
1313:Debye
1111:Zuber
961:Stora
926:Segal
906:Salam
891:Proca
886:Popov
861:Pauli
841:Oehme
831:Neveu
826:Nambu
811:Mills
701:Jaffe
676:Hagen
671:Higgs
646:Gupta
641:Gross
626:Glimm
606:Furry
576:Fierz
566:Fermi
561:Fayet
556:Fadin
541:Dyson
531:Dirac
496:Brout
471:Bethe
431:Adler
210:Tools
43:right
3645:MSSM
3352:ISBN
3291:2008
3253:PMID
3141:PMID
3029:ISBN
2822:ISBN
2795:ISBN
2768:ISBN
2605:and
2227:and
2085:The
1994:For
1968:U(1)
1396:Bose
1076:Yang
1046:Wick
1041:Weyl
1031:Wess
1011:Ward
716:Jost
666:Hepp
656:Haag
581:Fock
461:Bell
39:left
3743:SNO
3738:LHC
3733:INO
3245:doi
3190:doi
3133:doi
3076:doi
2996:doi
2974:626
2939:doi
2886:doi
2851:203
2505:.)
2477:or
2456:â 0
2414:= 0
2360:in
2328:).
2320:).
2155:GUT
2099:In
2035:In
1964:= 0
1478:of
1292:NPT
1284:NPH
1276:”VT
1268:NVT
1260:NVE
1096:Zee
781:Low
756:Lee
4594::
3282:.
3259:.
3251:.
3243:.
3235:.
3223:99
3221:.
3196:.
3188:.
3180:.
3168:82
3166:.
3139:.
3131:.
3121:41
3119:.
3109:;
3105:;
3074:.
3066:.
3054:68
3052:.
3002:.
2994:.
2986:.
2972:.
2968:.
2945:.
2937:.
2929:.
2917:80
2915:.
2892:.
2884:.
2874:19
2872:.
2868:.
2488:.
2445:(â
2165:.
1544:.
3819:e
3812:t
3805:v
3399:e
3392:t
3385:v
3293:.
3267:.
3247::
3239::
3229::
3204:.
3192::
3184::
3174::
3147:.
3135::
3127::
3082:.
3078::
3070::
3060::
3037:.
3010:.
2998::
2990::
2980::
2953:.
2941::
2933::
2923::
2900:.
2888::
2880::
2853:.
2830:.
2803:.
2776:.
2454:h
2449:)
2447:x
2443:m
2439:x
2437:(
2435:m
2430:x
2428:(
2426:m
2418:h
2412:h
2047:.
1979:Ξ
1972:Ξ
1962:Ί
1957:Ï
1953:Ξ
1944:)
1942:3
1940:(
1934:.
1917:i
1913:e
1907:2
1903:/
1899:5
1894:=
1867:)
1865:2
1863:(
1857:.
1842:4
1837:|
1828:|
1824:+
1819:2
1814:|
1805:|
1801:5
1795:=
1792:)
1786:(
1783:V
1754:)
1748:(
1745:V
1730:)
1728:1
1726:(
1709:.
1706:)
1700:(
1697:V
1665:=
1660:L
1613:.
1601:)
1595:(
1592:V
1460:e
1453:t
1446:v
1149:e
1142:t
1135:v
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
