836:
2804:
448:
25:
831:{\displaystyle {\begin{array}{lcl}{\mathcal {L}}&=&(D_{\mu }\phi )^{*}D^{\mu }\phi -V(\phi ^{*}\phi )-{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\\&=&(\partial _{\mu }\phi )^{*}(\partial ^{\mu }\phi )-ie((\partial _{\mu }\phi )^{*}\phi -\phi ^{*}(\partial _{\mu }\phi ))A^{\mu }+e^{2}A_{\mu }A^{\mu }\phi ^{*}\phi -V(\phi ^{*}\phi )-{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\end{array}}}
1356:
923:
398:
1457:
1687:
1003:
1200:
1801:
316:
1206:
1577:
dimensions, admits time-independent finite energy configurations corresponding to vortices carrying magnetic flux. The magnetic flux carried by these vortices are quantized (in units of
1609:
263:
1873:
1110:
2152:
2128:
1840:
433:
1978:
1501:. This can be seen by studying fluctuations about the lowest energy configuration: one sees that the gauge field behaves as a massive field with its mass proportional to
1148:
1069:
225:
2005:
1383:
189:
1893:
1549:
1495:
2096:
2052:
1956:
1023:
1936:
1575:
1459:
In physics, it is customary to work under an implicit choice of trivialization, hence a gauge transformation really can be viewed as a change of trivialization.
2072:
2025:
1519:
1691:
These vortices are similar to the vortices appearing in type-II superconductors. This analogy was used by
Nielsen and Olesen in obtaining their solutions.
400:. The theory can also be defined for curved spacetime but these definitions must be replaced with a more subtle one. The gauge field is also known as a
846:
321:
2234:
1388:
1616:
2657:
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934:
1153:
2549:
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1705:
272:
89:
2287:
1351:{\displaystyle \phi '(x)=e^{ie\lambda (x)}\phi (x)\quad {\textrm {and}}\quad A_{\mu }'(x)=A_{\mu }(x)+\partial _{\mu }\lambda (x).}
61:
42:
2312:
68:
2647:
2416:
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2227:
145:. The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the
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108:
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57:
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46:
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1580:
146:
233:
2345:
1845:
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2133:
2109:
82:
2749:
1809:
407:
1961:
1385:
is an infinitesimal change of trivialization, which generates the finite change of trivialization
2621:
2477:
2446:
2421:
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1029:
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142:
35:
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2267:
1983:
1368:
165:
2761:
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2426:
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2335:
1904:
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1524:
1470:
2702:
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2081:
2037:
1941:
1008:
401:
1912:
8:
2766:
2732:
2667:
2585:
2575:
2370:
1842:, which is chosen to be greater than zero. This produces a circle of minima, with values
1554:
122:
2181:
2400:
2057:
2010:
1504:
2451:
2203:
2189:
453:
2722:
2185:
2744:
2482:
2431:
1498:
266:
918:{\displaystyle F_{\mu \nu }=(\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu })}
2687:
2662:
2441:
2103:
926:
393:{\displaystyle A_{\mu }:\mathbb {R} ^{1,3}\rightarrow (\mathbb {R} ^{1,3})^{*}}
1611:) and appears as a topological charge associated with the topological current
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2099:
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2168:
H. B. Nielsen and P. Olesen (1973). "Vortex-line models for dual strings".
2075:
1452:{\displaystyle e^{ie\lambda }:\mathbb {R} ^{1,3}\rightarrow {\text{U}}(1).}
134:
2385:
2212:
2155:
1682:{\displaystyle J_{top}^{\mu }=\epsilon ^{\mu \nu \rho }F_{\nu \rho }\ .}
1699:
A simple choice of potential for demonstrating the Higgs mechanism is
1467:
If the potential is such that its minimum occurs at non-zero value of
2518:
2028:
1121:
This model is invariant under gauge transformations parameterized by
998:{\displaystyle D_{\mu }\phi =(\partial _{\mu }\phi -ieA_{\mu }\phi )}
1195:{\displaystyle \lambda :\mathbb {R} ^{1,3}\rightarrow \mathbb {R} .}
24:
2616:
2078:; the label of "scalar" field refers only to the transformation of
1796:{\displaystyle V(|\phi |^{2})=\lambda (|\phi |^{2}-\Phi ^{2})^{2}.}
2102:, so it is still referred to as a scalar field, in the sense of a
311:{\displaystyle \phi :\mathbb {R} ^{1,3}\rightarrow \mathbb {C} }
2167:
1551:. As shown in 1973 by Nielsen and Olesen, this model, in
269:) so these fields can be treated (naĂŻvely) as functions
2054:
is valued in a representation space of the gauge group
2007:
to a theory with gauge symmetry under the gauge group
1585:
2136:
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This article discusses the theory on flat spacetime
49:. Unsourced material may be challenged and removed.
2146:
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1999:
1972:
1950:
1930:
1909:This theory can be generalized from a theory with
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427:
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257:
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183:
2818:
443:The dynamics is given by the Lagrangian density
152:
1360:
1112:is the potential for the complex scalar field.
2228:
162:The model consists of a complex scalar field
2242:
2235:
2221:
925:is the electromagnetic field strength, or
1966:
1938:gauge symmetry containing a scalar field
1413:
1185:
1165:
1005:is the covariant derivative of the field
364:
340:
304:
284:
239:
109:Learn how and when to remove this message
1898:
2200:An Introduction to Quantum Field Theory
2819:
2313:Two-dimensional conformal field theory
2216:
47:adding citations to reliable sources
18:
2139:
2115:
1604:{\displaystyle {\tfrac {2\pi }{e}}}
1116:
191:minimally coupled to a gauge field
16:Electrodynamics of spin 0 particles
13:
1849:
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258:{\displaystyle \mathbb {R} ^{1,3}}
14:
2838:
2808:Template:Quantum mechanics topics
1868:{\displaystyle \Phi e^{i\theta }}
1150:. This is a real-valued function
1105:{\displaystyle V(\phi ^{*}\phi )}
157:
2803:
2802:
23:
2147:{\displaystyle {\mathfrak {g}}}
2123:{\displaystyle {\mathfrak {g}}}
1275:
1267:
34:needs additional citations for
1925:
1919:
1822:
1814:
1806:The potential is minimized at
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1365:From the geometric viewpoint,
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1:
2198:Peskin, M and Schroeder, D.;
2161:
1835:{\displaystyle |\phi |=\Phi }
438:
428:{\displaystyle {\text{U}}(1)}
153:Matter content and Lagrangian
2190:10.1016/0550-3213(73)90350-7
1973:{\displaystyle \mathbb {C} }
137:that takes the place of the
133:coupled to a charged spin 0
7:
2772:Quantum information science
1521:times the minimum value of
1361:Differential-geometric view
1143:{\displaystyle \lambda (x)}
1064:{\displaystyle e=-|e|<0}
404:, specifically a principal
220:{\displaystyle A_{\mu }(x)}
10:
2843:
1902:
1694:
1497:, this model exhibits the
2797:
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2630:
2609:
2558:
2532:
2496:
2460:
2409:
2328:
2321:
2250:
1980:coupled to a gauge field
2098:under the action of the
2000:{\displaystyle A_{\mu }}
1378:{\displaystyle \lambda }
184:{\displaystyle \phi (x)}
58:"Scalar electrodynamics"
2827:Quantum electrodynamics
2468:2D free massless scalar
2361:Quantum electrodynamics
2288:QFT in curved spacetime
2202:(Westview Press, 1995)
2106:. The gauge-field is a
1888:{\displaystyle \theta }
1544:{\displaystyle |\phi |}
1490:{\displaystyle |\phi |}
147:Abelian Higgs mechanism
143:quantum electrodynamics
2789:Quantum thermodynamics
2713:On shell and off shell
2708:Loop quantum cosmology
2550:N = 4 super Yang–Mills
2509:N = 1 super Yang–Mills
2376:Scalar electrodynamics
2366:Quantum chromodynamics
2268:Conformal field theory
2244:Quantum field theories
2148:
2130:-valued 1-form, where
2124:
2092:
2068:
2048:
2021:
2001:
1974:
1952:
1932:
1889:
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1836:
1797:
1683:
1605:
1571:
1545:
1515:
1491:
1453:
1379:
1352:
1196:
1144:
1106:
1071:is the electric charge
1065:
1019:
999:
919:
832:
429:
394:
312:
259:
221:
185:
129:is a theory of a U(1)
127:scalar electrodynamics
2762:Quantum hydrodynamics
2757:Quantum hadrodynamics
2381:Scalar chromodynamics
2149:
2125:
2093:
2091:{\displaystyle \phi }
2069:
2049:
2047:{\displaystyle \phi }
2022:
2002:
1975:
1953:
1951:{\displaystyle \phi }
1933:
1905:scalar chromodynamics
1899:Scalar chromodynamics
1890:
1870:
1837:
1798:
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1606:
1572:
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1516:
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1353:
1197:
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1107:
1066:
1020:
1018:{\displaystyle \phi }
1000:
920:
833:
430:
395:
313:
260:
222:
186:
2733:Quantum fluctuations
2703:Loop quantum gravity
2273:Lattice field theory
2134:
2110:
2082:
2058:
2038:
2011:
1984:
1962:
1942:
1931:{\displaystyle U(1)}
1913:
1879:
1846:
1810:
1706:
1617:
1581:
1555:
1525:
1505:
1471:
1389:
1369:
1207:
1154:
1125:
1077:
1030:
1009:
935:
847:
449:
408:
402:principal connection
322:
273:
234:
195:
166:
43:improve this article
2767:Quantum information
2371:Quartic interaction
2182:1973NuPhB..61...45N
1640:
1570:{\displaystyle 2+1}
1288:
123:theoretical physics
2653:Nambu–Jona-Lasinio
2581:Higher dimensional
2488:Wess–Zumino–Witten
2278:Noncommutative QFT
2144:
2120:
2088:
2064:
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2017:
1997:
1970:
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1928:
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1865:
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1541:
1511:
1487:
1449:
1375:
1348:
1276:
1192:
1140:
1102:
1061:
1015:
995:
929:of the connection.
915:
828:
826:
425:
390:
308:
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217:
181:
2814:
2813:
2676:
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2170:Nuclear Physics B
2067:{\displaystyle G}
2034:The scalar field
2020:{\displaystyle G}
1675:
1598:
1514:{\displaystyle e}
1435:
1272:
796:
545:
414:
119:
118:
111:
93:
2834:
2806:
2805:
2723:Quantum dynamics
2396:Yang–Mills–Higgs
2351:Non-linear sigma
2341:Euler–Heisenberg
2326:
2325:
2237:
2230:
2223:
2214:
2213:
2193:
2153:
2151:
2150:
2145:
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2142:
2129:
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2119:
2118:
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2018:
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1600:
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1573:
1568:
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1520:
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1512:
1496:
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1201:
1199:
1198:
1193:
1188:
1180:
1179:
1168:
1149:
1147:
1146:
1141:
1117:Gauge-invariance
1111:
1109:
1108:
1103:
1095:
1094:
1070:
1068:
1067:
1062:
1054:
1046:
1024:
1022:
1021:
1016:
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1002:
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996:
988:
987:
966:
965:
947:
946:
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922:
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861:
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756:
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745:
736:
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713:
712:
694:
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681:
680:
665:
664:
652:
651:
621:
620:
608:
607:
595:
594:
576:
572:
571:
559:
558:
546:
538:
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526:
505:
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434:
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415:
412:
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367:
355:
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343:
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317:
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299:
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287:
264:
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261:
256:
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190:
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182:
114:
107:
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100:
94:
92:
51:
27:
19:
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2833:
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2810:
2793:
2745:Quantum gravity
2672:
2631:Particle theory
2626:
2605:
2554:
2528:
2492:
2456:
2410:Low dimensional
2405:
2346:Ginzburg–Landau
2317:
2308:Topological QFT
2246:
2241:
2164:
2138:
2137:
2135:
2132:
2131:
2114:
2113:
2111:
2108:
2107:
2083:
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2079:
2059:
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2055:
2039:
2036:
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2012:
2009:
2008:
1991:
1987:
1985:
1982:
1981:
1965:
1963:
1960:
1959:
1943:
1940:
1939:
1914:
1911:
1910:
1907:
1901:
1895:a real number.
1880:
1877:
1876:
1856:
1852:
1847:
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1843:
1821:
1813:
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1808:
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1536:
1528:
1526:
1523:
1522:
1506:
1503:
1502:
1499:Higgs mechanism
1482:
1474:
1472:
1469:
1468:
1465:
1463:Higgs mechanism
1432:
1417:
1412:
1411:
1396:
1392:
1390:
1387:
1386:
1370:
1367:
1366:
1363:
1327:
1323:
1305:
1301:
1280:
1269:
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1234:
1230:
1210:
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1184:
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1126:
1123:
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1119:
1090:
1086:
1078:
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1050:
1042:
1031:
1028:
1027:
1010:
1007:
1006:
983:
979:
961:
957:
942:
938:
936:
933:
932:
906:
902:
896:
892:
883:
879:
873:
869:
854:
850:
848:
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844:
825:
824:
815:
811:
802:
798:
788:
773:
769:
751:
747:
741:
737:
731:
727:
721:
717:
708:
704:
689:
685:
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660:
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616:
612:
603:
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500:
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486:
477:
473:
468:
463:
457:
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450:
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446:
441:
411:
409:
406:
405:
384:
380:
368:
363:
362:
344:
339:
338:
329:
325:
323:
320:
319:
303:
288:
283:
282:
274:
271:
270:
267:Minkowski space
243:
238:
237:
235:
232:
231:
202:
198:
196:
193:
192:
167:
164:
163:
160:
155:
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
2840:
2830:
2829:
2812:
2811:
2798:
2795:
2794:
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2791:
2786:
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2769:
2764:
2759:
2754:
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2752:
2742:
2741:
2740:
2730:
2725:
2720:
2715:
2710:
2705:
2700:
2695:
2690:
2688:Casimir effect
2684:
2682:
2678:
2677:
2674:
2673:
2671:
2670:
2665:
2663:Standard Model
2660:
2655:
2650:
2645:
2640:
2634:
2632:
2628:
2627:
2625:
2624:
2619:
2613:
2611:
2607:
2606:
2604:
2603:
2598:
2593:
2588:
2583:
2578:
2573:
2568:
2562:
2560:
2556:
2555:
2553:
2552:
2547:
2542:
2536:
2534:
2533:Superconformal
2530:
2529:
2527:
2526:
2521:
2516:
2514:Seiberg–Witten
2511:
2506:
2500:
2498:
2497:Supersymmetric
2494:
2493:
2491:
2490:
2485:
2480:
2475:
2470:
2464:
2462:
2458:
2457:
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2454:
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2398:
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2348:
2343:
2338:
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2319:
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2315:
2310:
2305:
2300:
2295:
2290:
2285:
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2275:
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2260:
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2248:
2247:
2240:
2239:
2232:
2225:
2217:
2211:
2210:
2195:
2194:
2163:
2160:
2141:
2117:
2104:Lorentz scalar
2087:
2074:, making it a
2063:
2043:
2016:
1994:
1990:
1968:
1947:
1927:
1924:
1921:
1918:
1900:
1897:
1884:
1862:
1859:
1855:
1851:
1831:
1828:
1824:
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1816:
1804:
1803:
1792:
1787:
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1750:
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1727:
1722:
1718:
1714:
1711:
1696:
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1670:
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1657:
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1638:
1633:
1630:
1627:
1623:
1597:
1593:
1590:
1566:
1563:
1560:
1539:
1535:
1531:
1510:
1485:
1481:
1477:
1464:
1461:
1448:
1445:
1442:
1439:
1431:
1426:
1423:
1420:
1415:
1410:
1405:
1402:
1399:
1395:
1374:
1362:
1359:
1347:
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1341:
1338:
1335:
1330:
1326:
1322:
1319:
1316:
1313:
1308:
1304:
1300:
1297:
1294:
1291:
1287:
1283:
1279:
1266:
1263:
1260:
1257:
1252:
1249:
1246:
1243:
1240:
1237:
1233:
1229:
1226:
1223:
1220:
1216:
1213:
1191:
1187:
1183:
1178:
1175:
1172:
1167:
1162:
1159:
1139:
1136:
1133:
1130:
1118:
1115:
1114:
1113:
1101:
1098:
1093:
1089:
1085:
1082:
1072:
1060:
1057:
1053:
1049:
1045:
1041:
1038:
1035:
1025:
1014:
994:
991:
986:
982:
978:
975:
972:
969:
964:
960:
956:
953:
950:
945:
941:
930:
914:
909:
905:
899:
895:
891:
886:
882:
876:
872:
868:
865:
860:
857:
853:
821:
818:
814:
808:
805:
801:
795:
792:
787:
784:
781:
776:
772:
768:
765:
762:
759:
754:
750:
744:
740:
734:
730:
724:
720:
716:
711:
707:
703:
700:
697:
692:
688:
684:
679:
675:
671:
668:
663:
659:
655:
650:
646:
642:
639:
636:
633:
630:
627:
624:
619:
615:
611:
606:
602:
598:
593:
589:
585:
582:
580:
577:
575:
570:
567:
563:
557:
554:
550:
544:
541:
536:
533:
530:
525:
521:
517:
514:
511:
508:
503:
499:
493:
489:
485:
480:
476:
472:
469:
467:
464:
460:
455:
454:
440:
437:
424:
421:
418:
387:
383:
377:
374:
371:
366:
361:
358:
353:
350:
347:
342:
337:
332:
328:
306:
302:
297:
294:
291:
286:
281:
278:
252:
249:
246:
241:
216:
213:
210:
205:
201:
180:
177:
174:
171:
159:
158:Matter content
156:
154:
151:
141:in "ordinary"
139:Dirac fermions
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2839:
2828:
2825:
2824:
2822:
2809:
2801:
2796:
2790:
2787:
2785:
2784:Quantum logic
2782:
2778:
2775:
2774:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2751:
2748:
2747:
2746:
2743:
2739:
2736:
2735:
2734:
2731:
2729:
2726:
2724:
2721:
2719:
2718:Quantum chaos
2716:
2714:
2711:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2693:Cosmic string
2691:
2689:
2686:
2685:
2683:
2679:
2669:
2666:
2664:
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2636:
2635:
2633:
2629:
2623:
2620:
2618:
2615:
2614:
2612:
2608:
2602:
2599:
2597:
2594:
2592:
2589:
2587:
2584:
2582:
2579:
2577:
2574:
2572:
2569:
2567:
2566:Pure 4D N = 1
2564:
2563:
2561:
2557:
2551:
2548:
2546:
2543:
2541:
2538:
2537:
2535:
2531:
2525:
2522:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2501:
2499:
2495:
2489:
2486:
2484:
2481:
2479:
2476:
2474:
2471:
2469:
2466:
2465:
2463:
2459:
2453:
2450:
2448:
2447:Thirring–Wess
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2423:
2422:Bullough–Dodd
2420:
2418:
2417:2D Yang–Mills
2415:
2414:
2412:
2408:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
2367:
2364:
2362:
2359:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2333:
2331:
2327:
2324:
2320:
2314:
2311:
2309:
2306:
2304:
2301:
2299:
2296:
2294:
2293:String theory
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2264:
2263:Axiomatic QFT
2261:
2259:
2258:Algebraic QFT
2256:
2255:
2253:
2249:
2245:
2238:
2233:
2231:
2226:
2224:
2219:
2218:
2215:
2209:
2208:0-201-50397-2
2205:
2201:
2197:
2196:
2191:
2187:
2183:
2179:
2175:
2171:
2166:
2165:
2159:
2157:
2105:
2101:
2100:Lorentz group
2085:
2077:
2061:
2041:
2032:
2030:
2014:
1992:
1988:
1945:
1922:
1916:
1906:
1896:
1882:
1860:
1857:
1853:
1826:
1818:
1790:
1785:
1775:
1767:
1762:
1752:
1741:
1738:
1730:
1720:
1709:
1702:
1701:
1700:
1692:
1689:
1676:
1668:
1665:
1661:
1655:
1652:
1649:
1645:
1641:
1636:
1631:
1628:
1625:
1621:
1612:
1595:
1591:
1588:
1564:
1561:
1558:
1533:
1508:
1500:
1479:
1460:
1446:
1440:
1424:
1421:
1418:
1408:
1403:
1400:
1397:
1393:
1372:
1358:
1345:
1339:
1333:
1328:
1320:
1314:
1306:
1302:
1298:
1292:
1285:
1281:
1277:
1261:
1255:
1247:
1241:
1238:
1235:
1231:
1227:
1221:
1214:
1211:
1202:
1189:
1176:
1173:
1170:
1160:
1157:
1134:
1128:
1096:
1091:
1087:
1080:
1073:
1058:
1055:
1047:
1039:
1036:
1033:
1026:
1012:
989:
984:
980:
976:
973:
970:
967:
962:
951:
948:
943:
939:
931:
928:
907:
903:
897:
889:
884:
880:
874:
863:
858:
855:
851:
843:
842:
841:
838:
819:
816:
812:
806:
803:
799:
793:
790:
785:
779:
774:
770:
763:
760:
757:
752:
748:
742:
738:
732:
728:
722:
718:
714:
709:
705:
695:
690:
677:
673:
669:
666:
661:
653:
648:
634:
631:
628:
622:
617:
604:
596:
591:
578:
568:
565:
561:
555:
552:
548:
542:
539:
534:
528:
523:
519:
512:
509:
506:
501:
497:
491:
483:
478:
474:
465:
444:
436:
419:
403:
385:
375:
372:
369:
351:
348:
345:
335:
330:
326:
295:
292:
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228:
211:
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199:
175:
169:
150:
148:
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140:
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132:
128:
124:
113:
110:
102:
99:December 2007
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
2799:
2728:Quantum foam
2668:Stueckelberg
2622:Chern–Simons
2559:Supergravity
2375:
2298:Supergravity
2283:Gauge theory
2199:
2173:
2169:
2033:
1908:
1805:
1698:
1690:
1613:
1466:
1364:
1203:
1120:
839:
445:
442:
435:connection.
229:
161:
135:scalar field
130:
126:
120:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
2610:Topological
2524:Wess–Zumino
2437:Sine-Gordon
2427:Gross–Neveu
2336:Born–Infeld
2303:Thermal QFT
2156:Lie algebra
131:gauge field
2391:Yang–Mills
2162:References
1958:valued in
1903:See also:
439:Lagrangian
69:newspapers
2800:See also:
2519:Super QCD
2473:Liouville
2461:Conformal
2432:Schwinger
2176:: 45–61.
2086:ϕ
2042:ϕ
2029:Lie group
1993:μ
1946:ϕ
1883:θ
1861:θ
1850:Φ
1830:Φ
1819:ϕ
1772:Φ
1768:−
1753:ϕ
1742:λ
1721:ϕ
1669:ρ
1666:ν
1656:ρ
1653:ν
1650:μ
1646:ϵ
1637:μ
1592:π
1534:ϕ
1480:ϕ
1430:→
1404:λ
1373:λ
1334:λ
1329:μ
1325:∂
1307:μ
1282:μ
1256:ϕ
1242:λ
1212:ϕ
1182:→
1158:λ
1129:λ
1097:ϕ
1092:∗
1088:ϕ
1040:−
1013:ϕ
990:ϕ
985:μ
971:−
968:ϕ
963:μ
959:∂
949:ϕ
944:μ
927:curvature
908:μ
898:ν
894:∂
890:−
885:ν
875:μ
871:∂
859:ν
856:μ
820:ν
817:μ
807:ν
804:μ
786:−
780:ϕ
775:∗
771:ϕ
761:−
758:ϕ
753:∗
749:ϕ
743:μ
733:μ
710:μ
696:ϕ
691:μ
687:∂
678:∗
674:ϕ
670:−
667:ϕ
662:∗
654:ϕ
649:μ
645:∂
629:−
623:ϕ
618:μ
614:∂
605:∗
597:ϕ
592:μ
588:∂
569:ν
566:μ
556:ν
553:μ
535:−
529:ϕ
524:∗
520:ϕ
510:−
507:ϕ
502:μ
492:∗
484:ϕ
479:μ
386:∗
357:→
331:μ
301:→
277:ϕ
204:μ
170:ϕ
2821:Category
2596:Type IIB
2591:Type IIA
2576:4D N = 8
2571:4D N = 1
2540:6D (2,0)
2504:4D N = 1
2483:Polyakov
2442:Thirring
2251:Theories
1286:′
1215:′
2698:History
2681:Related
2478:Minimal
2329:Regular
2178:Bibcode
2154:is the
1695:Example
840:where
83:scholar
2638:Chiral
2586:Type I
2401:Yukawa
2322:Models
2206:
2158:of G.
2076:vector
1875:, for
1674:
318:, and
85:
78:
71:
64:
56:
2777:links
2750:links
2738:links
2658:NMSSM
2643:Fermi
2386:Soler
2356:Proca
90:JSTOR
76:books
2648:MSSM
2545:ABJM
2452:Toda
2204:ISBN
2027:, a
1056:<
62:news
2601:11D
2186:doi
1271:and
121:In
45:by
2823::
2617:BF
2184:.
2174:61
2172:.
2031:.
227:.
149:.
125:,
2236:e
2229:t
2222:v
2192:.
2188::
2180::
2140:g
2116:g
2062:G
2015:G
1989:A
1967:C
1926:)
1923:1
1920:(
1917:U
1858:i
1854:e
1827:=
1823:|
1815:|
1791:.
1786:2
1782:)
1776:2
1763:2
1758:|
1749:|
1745:(
1739:=
1736:)
1731:2
1726:|
1717:|
1713:(
1710:V
1677:.
1662:F
1642:=
1632:p
1629:o
1626:t
1622:J
1596:e
1589:2
1565:1
1562:+
1559:2
1538:|
1530:|
1509:e
1484:|
1476:|
1447:.
1444:)
1441:1
1438:(
1434:U
1425:3
1422:,
1419:1
1414:R
1409::
1401:e
1398:i
1394:e
1346:.
1343:)
1340:x
1337:(
1321:+
1318:)
1315:x
1312:(
1303:A
1299:=
1296:)
1293:x
1290:(
1278:A
1265:)
1262:x
1259:(
1251:)
1248:x
1245:(
1239:e
1236:i
1232:e
1228:=
1225:)
1222:x
1219:(
1190:.
1186:R
1177:3
1174:,
1171:1
1166:R
1161::
1138:)
1135:x
1132:(
1100:)
1084:(
1081:V
1059:0
1052:|
1048:e
1044:|
1037:=
1034:e
993:)
981:A
977:e
974:i
955:(
952:=
940:D
913:)
904:A
881:A
867:(
864:=
852:F
813:F
800:F
794:4
791:1
783:)
767:(
764:V
739:A
729:A
723:2
719:e
715:+
706:A
702:)
699:)
683:(
658:)
641:(
638:(
635:e
632:i
626:)
610:(
601:)
584:(
579:=
562:F
549:F
543:4
540:1
532:)
516:(
513:V
498:D
488:)
475:D
471:(
466:=
459:L
423:)
420:1
417:(
413:U
382:)
376:3
373:,
370:1
365:R
360:(
352:3
349:,
346:1
341:R
336::
327:A
305:C
296:3
293:,
290:1
285:R
280::
265:(
251:3
248:,
245:1
240:R
215:)
212:x
209:(
200:A
179:)
176:x
173:(
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
