Issues

 / 

1986

 / 

November

  

Reviews of topical problems


Anomalies in gauge theories


Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

In a quantum system with an infinite number of degrees of freedom, loop corrections may break symmetries of the original Lagrangian. This phenomenon, a ``quantum anomaly'', arises from the need for a ``regularization'': a supplemental definition of the theory in the ultraviolet region. A supplemental definition of this sort unavoidably runs into a contradiction with certain symmetries of the classical theory. In particular, it causes a nonconservation of corresponding Noether currents. Reasons for the appearance of anomalies and their place in the structure of modern field-theory models are discussed in this review. An emphasis is placed on anomalies in the internal currents of gauge theories. These anomalies may disrupt the invariance under infinitesimal or global gauge transformations, with the result that the theory is no longer self-consistent. The condition which must be met for the cancellation of internal anomalies severely restricts the composition of fields and the choice of interaction in realistic models. Methods for calculating anomalies are discussed in detail. Emphasis is placed on the nonconservation of axial and chiral fermion currents. The hierarchy of anomalies is introduced. A special section is devoted to global anomalies, in particular, Witten's SU(2) anomaly and a corresponding phenomenon in odd-dimensional Yang--Mills theories.

Fulltext pdf (2.1 MB)
Fulltext is also available at DOI: 10.1070/PU1986v029n11ABEH003537
PACS: 11.15.Ex, 11.55.Fv, 11.30.Ly, 11.30.Rd, 11.10.Gh (all)
DOI: 10.1070/PU1986v029n11ABEH003537
URL: https://ufn.ru/en/articles/1986/11/a/
Citation: Morozov A Yu "Anomalies in gauge theories" Sov. Phys. Usp. 29 993–1039 (1986)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Ìîðîçîâ À Þ «Àíîìàëèè â êàëèáðîâî÷íûõ òåîðèÿõ» ÓÔÍ 150 337–416 (1986); DOI: 10.3367/UFNr.0150.198611a.0337

Cited by (37) ↓ Similar articles (20)

  1. Jeong H, Kamada K et al J. Cosmol. Astropart. Phys. 2023 023 (2023)
  2. Lorcé C, Metz A et al J. High Energ. Phys. 2021 (11) (2021)
  3. Belokon A, Tokareva A Phys. Rev. D 101 (10) (2020)
  4. Itoyama H, Mironov A, Morozov A Nuclear Physics B 932 52 (2018)
  5. Zubkov M A, Khaidukov Z V Jetp Lett. 106 172 (2017)
  6. Gorbunov D, Tokareva A J. Cosmol. Astropart. Phys. 2013 021 (2013)
  7. Fursaev D, Vassilevich D Operators, Geometry and Quanta Theoretical And Mathematical Physics Chapter 8 (2011) p. 157
  8. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 157 208 (2008) [Morozov A Yu Theor Math Phys 157 1542 (2008)]
  9. Dolotin V V, Dolotin V V i dr Teor. Mat. Fiz. 156 3 (2008)
  10. Dolotin V, Morozov A, Shakirov Sh Physics Letters B 651 71 (2007)
  11. Marshakov A V Uspekhi Fizicheskikh Nauk 172 977 (2002)
  12. Alekseev A, Mironov A, Morozov A Physics Letters B 532 350 (2002)
  13. Kucheryavy V I Nuclear Physics B - Proceedings Supplements 102-103 377 (2001)
  14. Franz M, Pobylitsa P V et al Physics Letters B 454 335 (1999)
  15. Rudolph G, Tok T, Volobuev I 40 5890 (1999)
  16. Vacaru S I Nuclear Physics B 494 590 (1997)
  17. Kirzhnits D A, Kirzhnits D A i dr Teor. Mat. Fiz. 109 124 (1996)
  18. Lenz F, Shifman M, Thies M Phys. Rev. D 51 7060 (1995)
  19. Shalaev B N Physics Reports 237 129 (1994)
  20. Shapiro I L, Jacksenaev A G Physics Letters B 324 286 (1994)
  21. Adam C, Bertlmann R A, Hofer P Riv. Nuovo Cim. 16 1 (1993)
  22. Khveshchenko D V Phys. Rev. B 48 15926 (1993)
  23. Hořejší Jiří Czech J Phys 42 241 (1992)
  24. Hořejší Jiří Czech J Phys 42 345 (1992)
  25. Morozov A Yu Uspekhi Fizicheskikh Nauk 162 83 (1992)
  26. Duncan M J, Kaloper N, Olive K A Nuclear Physics B 387 215 (1992)
  27. Dzhordzhadze G P, Sarishvili I T Theor Math Phys 93 1239 (1992)
  28. Tze Ch-H Symmetries in Science V Chapter 26 (1991) p. 527
  29. Kucheryavii V I Ukr Math J 43 1339 (1991)
  30. Rennie R Advances In Physics 39 617 (1990)
  31. Krive I V, Latinskii S M Theor Math Phys 82 267 (1990)
  32. Pittori C, Testa M Z. Phys. C - Particles And Fields 47 487 (1990)
  33. Nyeo S-L Lecture Notes In Physics Vol. Physical and Nonstandard GaugesRegularization and Feynman rules in noncovariant gauges361 Chapter 17 (1990) p. 150
  34. Ketov S V Class. Quantum Grav. 7 1387 (1990)
  35. Hořejší J, Zavialov O I Czech J Phys 39 478 (1989)
  36. Zharkov V M Theor Math Phys 77 1077 (1988)
  37. Smilga A V Physics Letters B 199 516 (1987)

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions