3698:
442:(spin 1, Yukawa-like interaction) yields a force that is attractive between opposite charge and repulsive between like-charge.) The negative sign in the exponential gives the interaction a finite effective range, so that particles at great distances will hardly interact any longer (interaction forces fall off exponentially with increasing separation).
401:
except for the sign and the exponential factor. The sign will make the interaction attractive between all particles (the electromagnetic interaction is repulsive for same electrical charge sign particles). This is explained by the fact that the Yukawa particle has spin zero and even spin always
1308:
1187:
1636:
1858:
473:
part results from the dilution of the field line flux in space. The force is proportional to the number of field lines crossing an elementary surface. Since the field lines are emitted isotropically from the force source and since the distance
1738:
393:
2339:, this non-zero expectation is responsible for the fermion masses despite the chiral symmetry of the model apparently excluding them. To exhibit the mass term, the action can be re-expressed in terms of the derived field
1520:
2582:
The Yukawa coupling for any given fermion in the
Standard Model is an input to the theory. The ultimate reason for these couplings is not known: it would be something that a better, deeper theory should explain.
1198:
2268:
2595:. In fact, the Yukawa interaction involving a scalar and a Dirac spinor can be thought of as a Yukawa interaction involving a scalar with two Majorana spinors of the same mass. Broken out in terms of the two
809:
185:
1415:
1536:
119:
743:
1755:
2474:
2068:
2891:
2387:
1070:
1088:
1650:
2545:
2573:
2192:
583:
2420:
2156:
2121:
1345:
2505:
3128:
2331:
2298:
307:
874:
847:
1435:
296:
3551:
3361:
3443:
3402:
637:
potentials because they interact with each other, distorting their field pattern. When this self-interaction is negligible, such as in weak-field gravity (
3181:
1444:
3206:
3310:
3541:
3433:
3121:
2425:
3289:
3171:
2197:
678:
51:
3010:
1867:
758:
134:
3701:
3381:
3097:
3071:
3041:
2602:
881:
3631:
3438:
3201:
3234:
1350:
3591:
3494:
3474:
3114:
74:
1303:{\displaystyle {\mathcal {L}}_{\mathrm {meson} }(\phi )={\frac {1}{2}}\partial ^{\mu }\phi \;\partial _{\mu }\phi -V(\phi )~.}
701:
3397:
3156:
3151:
3720:
2271:
2082:
245:
3546:
3670:
3196:
3730:
3665:
3459:
3239:
546:) of the mesons causes a reduction of the flux through the surface that results in the additional exponential factor
542:
part of the potential. In addition, the exchanged mesons are unstable and have a finite lifetime. The disappearance (
1182:{\displaystyle \mathrm {d} ^{4}x\equiv \mathrm {d} x_{1}\,\mathrm {d} x_{2}\,\mathrm {d} x_{3}\,\mathrm {d} x_{4}~.}
3407:
1631:{\displaystyle {\mathcal {L}}_{\mathrm {Dirac} }(\psi )={\bar {\psi }}\,\left(i\,\partial \!\!\!/-m\right)\,\psi }
1192:
2422:
is constructed to be independent of position (a constant). This means that the Yukawa term includes a component
1853:{\displaystyle {\mathcal {L}}_{\mathrm {Yukawa} }(\phi ,\psi )=-g\,{\bar {\psi }}\,i\,\gamma ^{5}\,\phi \,\psi }
3643:
2301:
249:
3515:
3340:
3315:
2342:
3725:
3371:
3254:
2547:
This mechanism is the means by which spontaneous symmetry breaking gives mass to fermions. The scalar field
3682:
3606:
3601:
3536:
3464:
3366:
3269:
3259:
3244:
3161:
3417:
3320:
3284:
3229:
3655:
3650:
3489:
3484:
3274:
638:
435:
445:
As for other forces, the form of the Yukawa potential has a geometrical interpretation in term of the
3596:
3330:
3166:
3137:
2973:
2935:
2510:
403:
3660:
3626:
3561:
3479:
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3264:
2596:
1527:
2161:
549:
2392:
646:
642:
427:
198:
2126:
2091:
1733:{\displaystyle {\mathcal {L}}_{\mathrm {Yukawa} }(\phi ,\psi )=-g\,{\bar {\psi }}\,\phi \,\psi }
1315:
2483:
3345:
3093:
3067:
3037:
3006:
2900:
2307:
1747:
543:
398:
2550:
2277:
3616:
3051:
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2926:
1862:
for pseudoscalar mesons. Putting it all together one can write the above more explicitly as
822:
265:
47:
31:
859:
832:
478:
between the elementary surface and the source varies the apparent size of the surface (the
3638:
3376:
3325:
3025:
2939:
1420:
281:
253:
2977:
3581:
3556:
3335:
3086:
3081:
3060:
3030:
2908:
2592:
2336:
1438:
225:
3714:
3677:
3611:
3586:
3186:
2507:
are constants, the term presents as a mass term for the fermion with equivalent mass
206:
43:
3621:
3531:
3249:
3191:
3176:
3055:
1526:
is a coupling constant. This potential is explored in detail in the article on the
815:
682:
191:
55:
3279:
2986:
2961:
2576:
2078:
850:
690:
479:
388:{\displaystyle V(r)=-{\frac {g^{2}}{\,4\pi \,}}\,{\frac {1}{\,r\,}}\,e^{-\mu r}}
229:
63:
2085:
in the
Standard Model is responsible for fermion masses in a symmetric manner.
17:
446:
1515:{\textstyle V(\phi )={\frac {1}{2}}\,\mu ^{2}\,\phi ^{2}+\lambda \,\phi ^{4}}
3412:
614:
439:
1347:
is a self-interaction term. For a free-field massive meson, one would have
3510:
3106:
415:
2591:
It is also possible to have a Yukawa interaction between a scalar and a
586:
450:
419:
271:
252:
of the Higgs field. This Higgs-fermion coupling was first described by
241:
210:
202:
422:) results in forces always attractive, while odd-spin bosons like the
853:
610:
431:
423:
407:
237:
402:
results in an attractive potential. (It is a non-trivial result of
2263:{\displaystyle ~V(\phi )=\lambda \,\phi ^{4}~-\mu ^{2}\,\phi ^{2}}
826:
233:
218:
609:
potentials. (Note however that other massless particles such as
411:
214:
3110:
804:{\displaystyle g\,{\bar {\psi }}\,i\,\gamma ^{5}\,\phi \,\psi }
180:{\displaystyle g\,{\bar {\psi }}\,i\,\gamma ^{5}\,\phi \,\psi }
2194:
This can happen, for example, with a potential form such as
1762:
1657:
1543:
1205:
998:
958:
918:
1410:{\textstyle ~V(\phi )={\frac {1}{2}}\,\mu ^{2}\,\phi ^{2}~}
114:{\displaystyle ~V\approx g\,{\bar {\psi }}\,\phi \,\psi }
738:{\displaystyle V\approx g\,{\bar {\psi }}\,\phi \,\psi }
298:, the potential between the two particles, known as the
46:, is an interaction between particles according to the
1901:
1447:
1353:
2605:
2553:
2513:
2486:
2469:{\displaystyle ~g\,\phi _{0}\,{\bar {\psi }}\,\psi ~}
2428:
2395:
2345:
2310:
2280:
2200:
2164:
2129:
2094:
1870:
1758:
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862:
835:
761:
704:
552:
310:
284:
137:
77:
2300:
field, when operating on the vacuum, has a non-zero
1441:, polynomial) self-interacting field, one will have
585:
of the Yukawa potential. Massless particles such as
274:
interact through a Yukawa interaction mediated by a
248:, these fermions acquire a mass proportional to the
205:. A Yukawa interaction is thus used to describe the
3574:
3524:
3503:
3452:
3426:
3390:
3354:
3303:
3222:
3215:
3144:
1078:dimensions; for typical four-dimensional spacetime
677:The Yukawa interaction is an interaction between a
3085:
3059:
3029:
2885:
2567:
2539:
2499:
2468:
2414:
2381:
2325:
2292:
2262:
2186:
2150:
2115:
2073:Yukawa coupling to the Higgs in the Standard Model
2062:
1852:
1732:
1644:is the real-valued, positive mass of the fermion.
1630:
1514:
1429:
1409:
1339:
1302:
1181:
1064:
868:
841:
803:
737:
577:
387:
290:
197:The Yukawa interaction was developed to model the
179:
113:
1985:
1984:
1983:
1607:
1606:
1605:
27:Type of interaction between scalars and fermions
2063:{\displaystyle S=\int \left\mathrm {d} ^{n}x~.}
3122:
2886:{\displaystyle S=\int \left\mathrm {d} ^{n}x}
1065:{\displaystyle S=\int \left\mathrm {d} ^{n}x}
8:
2274:. This is because the non-zero value of the
1533:The free-field Dirac Lagrangian is given by
522: dependence. This is equivalent to the
3219:
3129:
3115:
3107:
2660:
1926:
1265:
2985:
2874:
2869:
2862:
2856:
2851:
2845:
2840:
2834:
2829:
2823:
2815:
2802:
2792:
2785:
2779:
2774:
2768:
2763:
2756:
2743:
2733:
2723:
2719:
2708:
2707:
2706:
2702:
2696:
2665:
2651:
2646:
2636:
2635:
2604:
2552:
2525:
2520:
2512:
2491:
2485:
2459:
2448:
2447:
2446:
2440:
2435:
2427:
2403:
2394:
2367:
2344:
2309:
2279:
2254:
2249:
2243:
2227:
2222:
2199:
2172:
2163:
2128:
2093:
2045:
2040:
2033:
2029:
2025:
2014:
2013:
2012:
2002:
1986:
1979:
1970:
1959:
1958:
1931:
1917:
1912:
1900:
1869:
1846:
1842:
1836:
1831:
1827:
1816:
1815:
1814:
1768:
1767:
1761:
1760:
1757:
1726:
1722:
1711:
1710:
1709:
1663:
1662:
1656:
1655:
1652:
1624:
1608:
1601:
1592:
1581:
1580:
1549:
1548:
1542:
1541:
1538:
1506:
1501:
1489:
1484:
1478:
1473:
1463:
1446:
1422:
1398:
1393:
1387:
1382:
1372:
1352:
1317:
1270:
1256:
1242:
1211:
1210:
1204:
1203:
1200:
1167:
1158:
1157:
1151:
1142:
1141:
1135:
1126:
1125:
1119:
1110:
1098:
1093:
1090:
1053:
1048:
1041:
1004:
1003:
997:
996:
964:
963:
957:
956:
924:
923:
917:
916:
914:
883:
861:
834:
797:
793:
787:
782:
778:
767:
766:
765:
760:
731:
727:
716:
715:
714:
703:
560:
551:
373:
368:
364:
360:
354:
353:
349:
342:
335:
329:
309:
283:
224:A Yukawa interaction is also used in the
173:
169:
163:
158:
154:
143:
142:
141:
136:
107:
103:
92:
91:
90:
76:
2382:{\displaystyle \phi '=\phi -\phi _{0}~,}
2270:. In this case, the Lagrangian exhibits
1074:where the integration is performed over
3088:An Introduction to Quantum Field Theory
2952:
2915:is the number of dimensions, as above.
3207:Two-dimensional conformal field theory
641:) or for very short distances for the
228:to describe the coupling between the
7:
3005:(2nd ed.). World Scientific.
3003:Quantum Field Theory in a Nutshell
2870:
2724:
2662:
2648:
2041:
1980:
1928:
1914:
1784:
1781:
1778:
1775:
1772:
1769:
1679:
1676:
1673:
1670:
1667:
1664:
1602:
1562:
1559:
1556:
1553:
1550:
1437:is the mass for the meson. For a (
1267:
1253:
1224:
1221:
1218:
1215:
1212:
1159:
1143:
1127:
1111:
1094:
1049:
1020:
1017:
1014:
1011:
1008:
1005:
977:
974:
971:
968:
965:
937:
934:
931:
928:
925:
25:
3702:Template:Quantum mechanics topics
2930:provides a simple example of the
3697:
3696:
1647:The Yukawa interaction term is
256:in 1967 to model lepton masses.
50:. Specifically, it is between a
3084:; Schroeder, Daniel V. (1995).
2960:Weinberg, Steven (1967-11-20).
2942:involving a Yukawa interaction.
2540:{\displaystyle ~g\,\phi _{0}~.}
589:are stable and thus yield only
406:that the exchange of even-spin
3062:Relativistic Quantum Mechanics
3028:; Zuber, Jean-Bernard (1980).
2820:
2803:
2760:
2744:
2713:
2686:
2680:
2621:
2609:
2453:
2213:
2207:
2107:
2101:
2077:A Yukawa coupling term to the
2019:
1964:
1952:
1946:
1886:
1874:
1821:
1802:
1790:
1716:
1697:
1685:
1586:
1574:
1568:
1457:
1451:
1366:
1360:
1331:
1325:
1291:
1285:
1236:
1230:
1038:
1026:
989:
983:
949:
943:
900:
888:
772:
721:
414:(spin 0, Yukawa force) or the
320:
314:
240:fields (i.e., the fundamental
148:
97:
1:
2272:spontaneous symmetry breaking
2083:spontaneous symmetry breaking
246:spontaneous symmetry breaking
2187:{\displaystyle ~\phi _{0}~.}
578:{\displaystyle ~e^{-\mu r}~}
3666:Quantum information science
2987:10.1103/PhysRevLett.19.1264
2415:{\displaystyle ~\phi _{0}~}
2158:but at some non-zero value
2088:Suppose that the potential
502:the force also follows the
3747:
2599:Majorana spinors, one has
2151:{\displaystyle ~\phi =0~,}
2116:{\displaystyle ~V(\phi )~}
1340:{\displaystyle ~V(\phi )~}
263:
3691:
3066:. New York: McGraw-Hill.
3036:. New York: McGraw-Hill.
2500:{\displaystyle \phi _{0}}
2326:{\displaystyle ~\phi ~.}
2302:vacuum expectation value
2123:has its minimum, not at
669:potential is restored.)
250:vacuum expectation value
217:(which are pseudoscalar
3362:2D free massless scalar
3255:Quantum electrodynamics
3182:QFT in curved spacetime
2966:Physical Review Letters
2934:and a calculation of a
2568:{\displaystyle \phi '~}
2293:{\displaystyle ~\phi ~}
617:do not generally yield
397:which is the same as a
3683:Quantum thermodynamics
3607:On shell and off shell
3602:Loop quantum cosmology
3444:N = 4 super YangâMills
3403:N = 1 super YangâMills
3270:Scalar electrodynamics
3260:Quantum chromodynamics
3162:Conformal field theory
3138:Quantum field theories
3001:A. Zee (2010). "I.5".
2887:
2569:
2541:
2501:
2470:
2416:
2383:
2327:
2294:
2264:
2188:
2152:
2117:
2064:
1854:
1750:for scalar mesons and
1734:
1632:
1516:
1431:
1411:
1341:
1304:
1183:
1066:
870:
843:
805:
739:
579:
449:picture introduced by
389:
292:
181:
115:
3656:Quantum hydrodynamics
3651:Quantum hadrodynamics
3275:Scalar chromodynamics
2888:
2570:
2542:
2502:
2471:
2417:
2384:
2328:
2295:
2265:
2189:
2153:
2118:
2065:
1855:
1735:
1633:
1517:
1432:
1412:
1342:
1305:
1184:
1067:
871:
869:{\displaystyle \psi }
844:
842:{\displaystyle \phi }
806:
740:
639:Newtonian gravitation
580:
436:electromagnetic force
390:
293:
182:
116:
3721:Quantum field theory
3627:Quantum fluctuations
3597:Loop quantum gravity
3167:Lattice field theory
3032:Quantum Field Theory
2962:"A Model of Leptons"
2936:scattering amplitude
2603:
2551:
2511:
2484:
2426:
2393:
2343:
2308:
2278:
2198:
2162:
2127:
2092:
1868:
1756:
1651:
1537:
1445:
1430:{\displaystyle \mu }
1421:
1351:
1316:
1199:
1089:
882:
860:
833:
759:
702:
550:
404:quantum field theory
308:
291:{\displaystyle \mu }
282:
244:particles). Through
135:
75:
36:Yukawa's interaction
3661:Quantum information
3265:Quartic interaction
2978:1967PhRvL..19.1264W
1528:quartic interaction
849:interacting with a
260:Classical potential
3731:Electroweak theory
3547:NambuâJona-Lasinio
3475:Higher dimensional
3382:WessâZuminoâWitten
3172:Noncommutative QFT
3092:. Addison-Wesley.
3082:Peskin, Michael E.
2883:
2565:
2537:
2497:
2466:
2412:
2379:
2323:
2290:
2260:
2184:
2148:
2113:
2060:
1910:
1850:
1730:
1628:
1512:
1427:
1407:
1337:
1300:
1179:
1062:
866:
839:
801:
735:
647:asymptotic freedom
643:strong interaction
575:
428:strong interaction
385:
288:
177:
111:
3708:
3707:
3570:
3569:
3052:Bjorken, James D.
2972:(21): 1264â1266.
2901:coupling constant
2800:
2741:
2716:
2644:
2564:
2533:
2516:
2465:
2456:
2431:
2411:
2398:
2375:
2319:
2313:
2289:
2283:
2235:
2203:
2180:
2167:
2144:
2132:
2112:
2097:
2056:
2022:
1967:
1909:
1824:
1748:coupling constant
1719:
1589:
1471:
1406:
1380:
1356:
1336:
1321:
1296:
1250:
1175:
775:
724:
574:
555:
544:radioactive decay
399:Coulomb potential
366:
351:
151:
100:
80:
16:(Redirected from
3738:
3700:
3699:
3617:Quantum dynamics
3290:YangâMillsâHiggs
3245:Non-linear sigma
3235:EulerâHeisenberg
3220:
3131:
3124:
3117:
3108:
3103:
3091:
3077:
3065:
3056:Drell, Sidney D.
3047:
3035:
3026:Itzykson, Claude
3017:
3016:
2998:
2992:
2991:
2989:
2957:
2927:Yukawa potential
2914:
2906:
2898:
2892:
2890:
2889:
2884:
2879:
2878:
2873:
2867:
2863:
2861:
2860:
2850:
2849:
2839:
2838:
2828:
2827:
2801:
2793:
2784:
2783:
2773:
2772:
2742:
2734:
2718:
2717:
2709:
2701:
2700:
2670:
2669:
2656:
2655:
2645:
2637:
2575:is known as the
2574:
2572:
2571:
2566:
2562:
2561:
2546:
2544:
2543:
2538:
2531:
2530:
2529:
2514:
2506:
2504:
2503:
2498:
2496:
2495:
2479:
2476:and, since both
2475:
2473:
2472:
2467:
2463:
2458:
2457:
2449:
2445:
2444:
2429:
2421:
2419:
2418:
2413:
2409:
2408:
2407:
2396:
2388:
2386:
2385:
2380:
2373:
2372:
2371:
2353:
2332:
2330:
2329:
2324:
2317:
2311:
2299:
2297:
2296:
2291:
2287:
2281:
2269:
2267:
2266:
2261:
2259:
2258:
2248:
2247:
2233:
2232:
2231:
2201:
2193:
2191:
2190:
2185:
2178:
2177:
2176:
2165:
2157:
2155:
2154:
2149:
2142:
2130:
2122:
2120:
2119:
2114:
2110:
2095:
2069:
2067:
2066:
2061:
2054:
2050:
2049:
2044:
2038:
2034:
2024:
2023:
2015:
2001:
1997:
1990:
1969:
1968:
1960:
1936:
1935:
1922:
1921:
1911:
1902:
1859:
1857:
1856:
1851:
1841:
1840:
1826:
1825:
1817:
1789:
1788:
1787:
1766:
1765:
1745:
1739:
1737:
1736:
1731:
1721:
1720:
1712:
1684:
1683:
1682:
1661:
1660:
1643:
1637:
1635:
1634:
1629:
1623:
1619:
1612:
1591:
1590:
1582:
1567:
1566:
1565:
1547:
1546:
1525:
1521:
1519:
1518:
1513:
1511:
1510:
1494:
1493:
1483:
1482:
1472:
1464:
1436:
1434:
1433:
1428:
1416:
1414:
1413:
1408:
1404:
1403:
1402:
1392:
1391:
1381:
1373:
1354:
1346:
1344:
1343:
1338:
1334:
1319:
1309:
1307:
1306:
1301:
1294:
1275:
1274:
1261:
1260:
1251:
1243:
1229:
1228:
1227:
1209:
1208:
1188:
1186:
1185:
1180:
1173:
1172:
1171:
1162:
1156:
1155:
1146:
1140:
1139:
1130:
1124:
1123:
1114:
1103:
1102:
1097:
1084:
1077:
1071:
1069:
1068:
1063:
1058:
1057:
1052:
1046:
1042:
1025:
1024:
1023:
1002:
1001:
982:
981:
980:
962:
961:
942:
941:
940:
922:
921:
875:
873:
872:
867:
848:
846:
845:
840:
813:
810:
808:
807:
802:
792:
791:
777:
776:
768:
755:
751:
747:
744:
742:
741:
736:
726:
725:
717:
695:
688:
668:
667:
665:
664:
659:
656:
636:
635:
633:
632:
627:
624:
608:
607:
605:
604:
599:
596:
584:
582:
581:
576:
572:
571:
570:
553:
541:
540:
538:
537:
532:
529:
521:
520:
518:
517:
512:
509:
501:
500:
498:
497:
492:
489:
477:
472:
471:
469:
468:
463:
460:
394:
392:
391:
386:
384:
383:
367:
365:
355:
352:
350:
340:
339:
330:
300:Yukawa potential
297:
295:
294:
289:
266:Yukawa potential
189:
186:
184:
183:
178:
168:
167:
153:
152:
144:
131:
127:
123:
120:
118:
117:
112:
102:
101:
93:
78:
68:
61:
48:Yukawa potential
32:particle physics
21:
3746:
3745:
3741:
3740:
3739:
3737:
3736:
3735:
3711:
3710:
3709:
3704:
3687:
3639:Quantum gravity
3566:
3525:Particle theory
3520:
3499:
3448:
3422:
3386:
3350:
3304:Low dimensional
3299:
3240:GinzburgâLandau
3211:
3202:Topological QFT
3140:
3135:
3100:
3080:
3074:
3050:
3044:
3024:
3021:
3020:
3013:
3000:
2999:
2995:
2959:
2958:
2954:
2949:
2940:Feynman diagram
2921:
2912:
2904:
2896:
2868:
2852:
2841:
2830:
2819:
2775:
2764:
2692:
2661:
2647:
2634:
2630:
2601:
2600:
2589:
2554:
2549:
2548:
2521:
2509:
2508:
2487:
2482:
2481:
2477:
2436:
2424:
2423:
2399:
2391:
2390:
2363:
2346:
2341:
2340:
2306:
2305:
2276:
2275:
2250:
2239:
2223:
2196:
2195:
2168:
2160:
2159:
2125:
2124:
2090:
2089:
2075:
2039:
1975:
1971:
1927:
1913:
1899:
1895:
1866:
1865:
1832:
1759:
1754:
1753:
1743:
1654:
1649:
1648:
1641:
1597:
1593:
1540:
1535:
1534:
1523:
1502:
1485:
1474:
1443:
1442:
1419:
1418:
1394:
1383:
1349:
1348:
1314:
1313:
1266:
1252:
1202:
1197:
1196:
1163:
1147:
1131:
1115:
1092:
1087:
1086:
1079:
1075:
1047:
995:
955:
915:
913:
909:
880:
879:
858:
857:
831:
830:
819:
811:
783:
757:
756:
753:
749:
745:
700:
699:
693:
686:
675:
660:
657:
654:
653:
651:
650:
628:
625:
622:
621:
619:
618:
600:
597:
594:
593:
591:
590:
556:
548:
547:
533:
530:
527:
526:
524:
523:
513:
510:
507:
506:
504:
503:
493:
490:
487:
486:
484:
483:
475:
464:
461:
458:
457:
455:
454:
369:
359:
341:
331:
306:
305:
280:
279:
276:Yukawa particle
268:
262:
254:Steven Weinberg
195:
187:
159:
133:
132:
129:
125:
121:
73:
72:
66:
59:
40:Yukawa coupling
28:
23:
22:
18:Yukawa coupling
15:
12:
11:
5:
3744:
3742:
3734:
3733:
3728:
3726:Standard Model
3723:
3713:
3712:
3706:
3705:
3692:
3689:
3688:
3686:
3685:
3680:
3675:
3674:
3673:
3663:
3658:
3653:
3648:
3647:
3646:
3636:
3635:
3634:
3624:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3584:
3582:Casimir effect
3578:
3576:
3572:
3571:
3568:
3567:
3565:
3564:
3559:
3557:Standard Model
3554:
3549:
3544:
3539:
3534:
3528:
3526:
3522:
3521:
3519:
3518:
3513:
3507:
3505:
3501:
3500:
3498:
3497:
3492:
3487:
3482:
3477:
3472:
3467:
3462:
3456:
3454:
3450:
3449:
3447:
3446:
3441:
3436:
3430:
3428:
3427:Superconformal
3424:
3423:
3421:
3420:
3415:
3410:
3408:SeibergâWitten
3405:
3400:
3394:
3392:
3391:Supersymmetric
3388:
3387:
3385:
3384:
3379:
3374:
3369:
3364:
3358:
3356:
3352:
3351:
3349:
3348:
3343:
3338:
3333:
3328:
3323:
3318:
3313:
3307:
3305:
3301:
3300:
3298:
3297:
3292:
3287:
3282:
3277:
3272:
3267:
3262:
3257:
3252:
3247:
3242:
3237:
3232:
3226:
3224:
3217:
3213:
3212:
3210:
3209:
3204:
3199:
3194:
3189:
3184:
3179:
3174:
3169:
3164:
3159:
3154:
3148:
3146:
3142:
3141:
3136:
3134:
3133:
3126:
3119:
3111:
3105:
3104:
3098:
3078:
3072:
3048:
3042:
3019:
3018:
3012:978-0691140346
3011:
2993:
2951:
2950:
2948:
2945:
2944:
2943:
2920:
2917:
2909:complex number
2882:
2877:
2872:
2866:
2859:
2855:
2848:
2844:
2837:
2833:
2826:
2822:
2818:
2814:
2811:
2808:
2805:
2799:
2796:
2791:
2788:
2782:
2778:
2771:
2767:
2762:
2759:
2755:
2752:
2749:
2746:
2740:
2737:
2732:
2729:
2726:
2722:
2715:
2712:
2705:
2699:
2695:
2691:
2688:
2685:
2682:
2679:
2676:
2673:
2668:
2664:
2659:
2654:
2650:
2643:
2640:
2633:
2629:
2626:
2623:
2620:
2617:
2614:
2611:
2608:
2593:Majorana field
2588:
2585:
2560:
2557:
2536:
2528:
2524:
2519:
2494:
2490:
2462:
2455:
2452:
2443:
2439:
2434:
2406:
2402:
2378:
2370:
2366:
2362:
2359:
2356:
2352:
2349:
2337:Standard Model
2322:
2316:
2286:
2257:
2253:
2246:
2242:
2238:
2230:
2226:
2221:
2218:
2215:
2212:
2209:
2206:
2183:
2175:
2171:
2147:
2141:
2138:
2135:
2109:
2106:
2103:
2100:
2074:
2071:
2059:
2053:
2048:
2043:
2037:
2032:
2028:
2021:
2018:
2011:
2008:
2005:
2000:
1996:
1993:
1989:
1982:
1978:
1974:
1966:
1963:
1957:
1954:
1951:
1948:
1945:
1942:
1939:
1934:
1930:
1925:
1920:
1916:
1908:
1905:
1898:
1894:
1891:
1888:
1885:
1882:
1879:
1876:
1873:
1849:
1845:
1839:
1835:
1830:
1823:
1820:
1813:
1810:
1807:
1804:
1801:
1798:
1795:
1792:
1786:
1783:
1780:
1777:
1774:
1771:
1764:
1746:is the (real)
1729:
1725:
1718:
1715:
1708:
1705:
1702:
1699:
1696:
1693:
1690:
1687:
1681:
1678:
1675:
1672:
1669:
1666:
1659:
1627:
1622:
1618:
1615:
1611:
1604:
1600:
1596:
1588:
1585:
1579:
1576:
1573:
1570:
1564:
1561:
1558:
1555:
1552:
1545:
1509:
1505:
1500:
1497:
1492:
1488:
1481:
1477:
1470:
1467:
1462:
1459:
1456:
1453:
1450:
1439:renormalizable
1426:
1401:
1397:
1390:
1386:
1379:
1376:
1371:
1368:
1365:
1362:
1359:
1333:
1330:
1327:
1324:
1299:
1293:
1290:
1287:
1284:
1281:
1278:
1273:
1269:
1264:
1259:
1255:
1249:
1246:
1241:
1238:
1235:
1232:
1226:
1223:
1220:
1217:
1214:
1207:
1178:
1170:
1166:
1161:
1154:
1150:
1145:
1138:
1134:
1129:
1122:
1118:
1113:
1109:
1106:
1101:
1096:
1061:
1056:
1051:
1045:
1040:
1037:
1034:
1031:
1028:
1022:
1019:
1016:
1013:
1010:
1007:
1000:
994:
991:
988:
985:
979:
976:
973:
970:
967:
960:
954:
951:
948:
945:
939:
936:
933:
930:
927:
920:
912:
908:
905:
902:
899:
896:
893:
890:
887:
865:
838:
800:
796:
790:
786:
781:
774:
771:
764:
734:
730:
723:
720:
713:
710:
707:
698:
674:
671:
569:
566:
563:
559:
382:
379:
376:
372:
363:
358:
348:
345:
338:
334:
328:
325:
322:
319:
316:
313:
287:
264:Main article:
261:
258:
226:Standard Model
176:
172:
166:
162:
157:
150:
147:
140:
110:
106:
99:
96:
89:
86:
83:
71:
42:, named after
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3743:
3732:
3729:
3727:
3724:
3722:
3719:
3718:
3716:
3703:
3695:
3690:
3684:
3681:
3679:
3678:Quantum logic
3676:
3672:
3669:
3668:
3667:
3664:
3662:
3659:
3657:
3654:
3652:
3649:
3645:
3642:
3641:
3640:
3637:
3633:
3630:
3629:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3612:Quantum chaos
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3587:Cosmic string
3585:
3583:
3580:
3579:
3577:
3573:
3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3543:
3540:
3538:
3535:
3533:
3530:
3529:
3527:
3523:
3517:
3514:
3512:
3509:
3508:
3506:
3502:
3496:
3493:
3491:
3488:
3486:
3483:
3481:
3478:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3460:Pure 4D N = 1
3458:
3457:
3455:
3451:
3445:
3442:
3440:
3437:
3435:
3432:
3431:
3429:
3425:
3419:
3416:
3414:
3411:
3409:
3406:
3404:
3401:
3399:
3396:
3395:
3393:
3389:
3383:
3380:
3378:
3375:
3373:
3370:
3368:
3365:
3363:
3360:
3359:
3357:
3353:
3347:
3344:
3342:
3341:ThirringâWess
3339:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3319:
3317:
3316:BulloughâDodd
3314:
3312:
3311:2D YangâMills
3309:
3308:
3306:
3302:
3296:
3293:
3291:
3288:
3286:
3283:
3281:
3278:
3276:
3273:
3271:
3268:
3266:
3263:
3261:
3258:
3256:
3253:
3251:
3248:
3246:
3243:
3241:
3238:
3236:
3233:
3231:
3228:
3227:
3225:
3221:
3218:
3214:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3190:
3188:
3187:String theory
3185:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3158:
3157:Axiomatic QFT
3155:
3153:
3152:Algebraic QFT
3150:
3149:
3147:
3143:
3139:
3132:
3127:
3125:
3120:
3118:
3113:
3112:
3109:
3101:
3099:0-201-50397-2
3095:
3090:
3089:
3083:
3079:
3075:
3073:0-07-232002-8
3069:
3064:
3063:
3057:
3053:
3049:
3045:
3043:0-07-032071-3
3039:
3034:
3033:
3027:
3023:
3022:
3014:
3008:
3004:
2997:
2994:
2988:
2983:
2979:
2975:
2971:
2967:
2963:
2956:
2953:
2946:
2941:
2937:
2933:
2932:Feynman rules
2929:
2928:
2923:
2922:
2918:
2916:
2910:
2902:
2899:is a complex
2893:
2880:
2875:
2864:
2857:
2853:
2846:
2842:
2835:
2831:
2824:
2816:
2812:
2809:
2806:
2797:
2794:
2789:
2786:
2780:
2776:
2769:
2765:
2757:
2753:
2750:
2747:
2738:
2735:
2730:
2727:
2720:
2710:
2703:
2697:
2693:
2689:
2683:
2677:
2674:
2671:
2666:
2657:
2652:
2641:
2638:
2631:
2627:
2624:
2618:
2615:
2612:
2606:
2598:
2594:
2587:Majorana form
2586:
2584:
2580:
2578:
2558:
2555:
2534:
2526:
2522:
2517:
2492:
2488:
2460:
2450:
2441:
2437:
2432:
2404:
2400:
2376:
2368:
2364:
2360:
2357:
2354:
2350:
2347:
2338:
2333:
2320:
2314:
2303:
2284:
2273:
2255:
2251:
2244:
2240:
2236:
2228:
2224:
2219:
2216:
2210:
2204:
2181:
2173:
2169:
2145:
2139:
2136:
2133:
2104:
2098:
2086:
2084:
2080:
2072:
2070:
2057:
2051:
2046:
2035:
2030:
2026:
2016:
2009:
2006:
2003:
1998:
1994:
1991:
1987:
1976:
1972:
1961:
1955:
1949:
1943:
1940:
1937:
1932:
1923:
1918:
1906:
1903:
1896:
1892:
1889:
1883:
1880:
1877:
1871:
1863:
1860:
1847:
1843:
1837:
1833:
1828:
1818:
1811:
1808:
1805:
1799:
1796:
1793:
1751:
1749:
1740:
1727:
1723:
1713:
1706:
1703:
1700:
1694:
1691:
1688:
1645:
1638:
1625:
1620:
1616:
1613:
1609:
1598:
1594:
1583:
1577:
1571:
1531:
1529:
1507:
1503:
1498:
1495:
1490:
1486:
1479:
1475:
1468:
1465:
1460:
1454:
1448:
1440:
1424:
1399:
1395:
1388:
1384:
1377:
1374:
1369:
1363:
1357:
1328:
1322:
1310:
1297:
1288:
1282:
1279:
1276:
1271:
1262:
1257:
1247:
1244:
1239:
1233:
1194:
1189:
1176:
1168:
1164:
1152:
1148:
1136:
1132:
1120:
1116:
1107:
1104:
1099:
1082:
1072:
1059:
1054:
1043:
1035:
1032:
1029:
992:
986:
952:
946:
910:
906:
903:
897:
894:
891:
885:
877:
863:
855:
852:
836:
828:
824:
817:
798:
794:
788:
784:
779:
769:
762:
732:
728:
718:
711:
708:
705:
697:
692:
684:
680:
672:
670:
663:
648:
644:
640:
631:
616:
612:
603:
588:
567:
564:
561:
557:
545:
536:
516:
496:
481:
467:
452:
448:
443:
441:
437:
433:
429:
425:
421:
417:
413:
409:
405:
400:
395:
380:
377:
374:
370:
361:
356:
346:
343:
336:
332:
326:
323:
317:
311:
303:
301:
285:
277:
273:
267:
259:
257:
255:
251:
247:
243:
239:
235:
232:and massless
231:
227:
222:
220:
216:
212:
208:
207:nuclear force
204:
200:
193:
174:
170:
164:
160:
155:
145:
138:
108:
104:
94:
87:
84:
81:
70:
65:
57:
53:
49:
45:
44:Hideki Yukawa
41:
37:
33:
19:
3693:
3622:Quantum foam
3562:Stueckelberg
3516:ChernâSimons
3453:Supergravity
3294:
3192:Supergravity
3177:Gauge theory
3087:
3061:
3031:
3002:
2996:
2969:
2965:
2955:
2931:
2925:
2924:The article
2894:
2590:
2581:
2334:
2087:
2076:
1864:
1861:
1752:
1741:
1646:
1639:
1532:
1311:
1195:is given by
1190:
1080:
1073:
878:
820:
816:pseudoscalar
696:of the type
683:pseudoscalar
679:scalar field
676:
661:
629:
601:
534:
514:
494:
465:
444:
396:
304:
299:
275:
269:
223:
213:mediated by
199:strong force
196:
192:pseudoscalar
69:of the type
56:pseudoscalar
52:scalar field
39:
35:
29:
3504:Topological
3418:WessâZumino
3331:Sine-Gordon
3321:GrossâNeveu
3230:BornâInfeld
3197:Thermal QFT
2577:Higgs field
2079:Higgs field
691:Dirac field
480:solid angle
302:, will be:
230:Higgs field
64:Dirac field
3715:Categories
3285:YangâMills
2947:References
2081:effecting
1193:Lagrangian
1191:The meson
673:The action
447:field line
3694:See also:
3413:Super QCD
3367:Liouville
3355:Conformal
3326:Schwinger
2858:∗
2854:χ
2843:σ
2836:†
2832:χ
2825:∗
2817:ϕ
2790:−
2787:χ
2777:σ
2766:χ
2758:ϕ
2728:χ
2725:∂
2721:⋅
2714:¯
2711:σ
2698:†
2694:χ
2684:ϕ
2675:−
2672:ϕ
2667:μ
2663:∂
2658:ϕ
2653:μ
2649:∂
2628:∫
2619:χ
2613:ϕ
2556:ϕ
2523:ϕ
2489:ϕ
2461:ψ
2454:¯
2451:ψ
2438:ϕ
2401:ϕ
2365:ϕ
2361:−
2358:ϕ
2348:ϕ
2315:ϕ
2285:ϕ
2252:ϕ
2241:μ
2237:−
2225:ϕ
2220:λ
2211:ϕ
2170:ϕ
2134:ϕ
2105:ϕ
2031:ψ
2027:ϕ
2020:¯
2017:ψ
2007:−
2004:ψ
1992:−
1981:∂
1965:¯
1962:ψ
1950:ϕ
1941:−
1938:ϕ
1933:μ
1929:∂
1924:ϕ
1919:μ
1915:∂
1893:∫
1884:ψ
1878:ϕ
1848:ψ
1844:ϕ
1834:γ
1822:¯
1819:ψ
1809:−
1800:ψ
1794:ϕ
1728:ψ
1724:ϕ
1717:¯
1714:ψ
1704:−
1695:ψ
1689:ϕ
1626:ψ
1614:−
1603:∂
1587:¯
1584:ψ
1572:ψ
1504:ϕ
1499:λ
1487:ϕ
1476:μ
1455:ϕ
1425:μ
1396:ϕ
1385:μ
1364:ϕ
1329:ϕ
1289:ϕ
1280:−
1277:ϕ
1272:μ
1268:∂
1263:ϕ
1258:μ
1254:∂
1234:ϕ
1108:≡
1036:ψ
1030:ϕ
987:ψ
947:ϕ
907:∫
898:ψ
892:ϕ
864:ψ
837:ϕ
799:ψ
795:ϕ
785:γ
773:¯
770:ψ
748:(scalar)
733:ψ
729:ϕ
722:¯
719:ψ
709:≈
615:gravitons
565:μ
562:−
440:rho meson
438:) or the
434:(spin 1,
426:(spin 1,
418:(spin 2,
410:like the
378:μ
375:−
347:π
327:−
286:μ
175:ψ
171:ϕ
161:γ
149:¯
146:ψ
124:(scalar)
109:ψ
105:ϕ
98:¯
95:ψ
85:≈
3490:Type IIB
3485:Type IIA
3470:4D N = 8
3465:4D N = 1
3434:6D (2,0)
3398:4D N = 1
3377:Polyakov
3336:Thirring
3145:Theories
3058:(1964).
2919:See also
2559:′
2351:′
416:graviton
278:of mass
272:fermions
211:nucleons
209:between
201:between
3592:History
3575:Related
3372:Minimal
3223:Regular
2974:Bibcode
2938:from a
2335:In the
685:field)
666:
652:
649:), the
634:
620:
606:
592:
587:photons
539:
525:
519:
505:
499:
485:
470:
456:
451:Faraday
430:), the
420:gravity
270:If two
242:fermion
203:hadrons
58:field)
3532:Chiral
3480:Type I
3295:Yukawa
3216:Models
3096:
3070:
3040:
3009:
2911:, and
2895:where
2597:chiral
2563:
2532:
2515:
2464:
2430:
2410:
2397:
2389:where
2374:
2318:
2312:
2288:
2282:
2234:
2202:
2179:
2166:
2143:
2131:
2111:
2096:
2055:
1742:where
1640:where
1522:where
1417:where
1405:
1355:
1335:
1320:
1312:Here,
1295:
1174:
1085:, and
856:field
854:baryon
829:field
825:for a
823:action
812:
754:
750:
746:
689:and a
611:gluons
573:
554:
453:: The
432:photon
424:gluons
408:bosons
238:lepton
219:mesons
188:
130:
126:
122:
79:
62:and a
3671:links
3644:links
3632:links
3552:NMSSM
3537:Fermi
3280:Soler
3250:Proca
2907:is a
851:Dirac
827:meson
482:) as
234:quark
215:pions
3542:MSSM
3439:ABJM
3346:Toda
3094:ISBN
3068:ISBN
3038:ISBN
3007:ISBN
2480:and
821:The
681:(or
412:pion
236:and
54:(or
3495:11D
2982:doi
2304:of
1083:= 4
876:is
752:or
613:or
221:).
128:or
38:or
30:In
3717::
3511:BF
3054:;
2980:.
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3076:.
3046:.
3015:.
2990:.
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2976::
2913:n
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2897:g
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2876:n
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2847:2
2821:)
2813:g
2810:+
2807:m
2804:(
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2781:2
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2748:m
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2731:+
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2535:.
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2321:.
2256:2
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2208:(
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2140:0
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2099:V
2058:.
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2010:g
1999:)
1995:m
1988:/
1977:i
1973:(
1956:+
1953:)
1947:(
1944:V
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1897:[
1890:=
1887:]
1881:,
1875:[
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1838:5
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1812:g
1806:=
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1797:,
1791:(
1785:a
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1776:k
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1763:L
1744:g
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1698:)
1692:,
1686:(
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1617:m
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1569:(
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1496:+
1491:2
1480:2
1469:2
1466:1
1461:=
1458:)
1452:(
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1400:2
1389:2
1378:2
1375:1
1370:=
1367:)
1361:(
1358:V
1332:)
1326:(
1323:V
1298:.
1292:)
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1231:(
1225:n
1222:o
1219:s
1216:e
1213:m
1206:L
1177:.
1169:4
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1160:d
1153:3
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1121:1
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1100:4
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1033:,
1027:(
1021:a
1018:w
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1012:k
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999:L
993:+
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984:(
978:c
975:a
972:r
969:i
966:D
959:L
953:+
950:)
944:(
938:n
935:o
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919:L
911:[
904:=
901:]
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889:[
886:S
814:(
789:5
780:i
763:g
712:g
706:V
694:Ï
687:Ï
662:r
658:/
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645:(
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595:1
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466:r
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459:1
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357:1
344:4
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318:r
315:(
312:V
190:(
165:5
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67:Ï
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