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Communications in Mathematical Physics

, Volume 56, Issue 1, pp 57–78 | Cite as

Spontaneous symmetry breaking in local gauge quantum field theory; the Higgs mechanism

  • F. Strocchi
Article

Abstract

Spontaneous symmetry breakings in indefinite metric quantum field theories are analyzed and a generalization of the Goldstone theorem is proved. The case of local gauge quantum field theories is discussed in detail and a characterization is given of the occurrence of the Higgs mechanism versus the Goldstone mechanism. The Higgs phenomenon is explained on general grounds without the introduction of the so-called Higgs fields. The basic property is the relation between the local internal symmetry group and the local group of gauge transformations of the second kind. Spontaneous symmetry breaking ofc-number gauge transformations of the second kind is shown to always occur if there are charged local fields. The implications about the absence of mass gap in the Wightman functions and the occurrence of massless particles associated with the unbroken generators in the Higgs phenomenon are discussed.

Keywords

Quantum Field Theory Symmetry Group Gauge Transformation Quantum Computing Local Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Goldstone, J.: Nuovo Cimento19, 154 (1961);Google Scholar
  2. 1a.
    Nambu, Y., Jona-Lasinio, G.: Phys. Rev.122, 345 (1961)Google Scholar
  3. 2.
    Goldstone, J., Salam, A., Weinberg, S.: Phys. Rev.127, 965 (1961)Google Scholar
  4. 3.
    Kastler, D., Robinson, D., Swieca, J.: Commun. math. Phys.2, 108 (1966);Google Scholar
  5. 3a.
    Ezawa, H., Swieca, J.: Commun. math. Phys.5, 330 (1967)Google Scholar
  6. 4.
    Higgs, P.W.: Phys. Letters12, 132 (1964); Phys. Rev.145, 1156 (1966);Google Scholar
  7. 4a.
    Guralnik, G.S., Hagen, C.R., Kibble, T.W.B.: Phys. Rev. Letters13, 585 (1964); Kibble, T.W.B.: Phys. Rev.155, 1554 (1967);Google Scholar
  8. 4b.
    Englert, F., Brout, R.: Phys. Rev. Letters13, 321 (1964)Google Scholar
  9. 5.
    Streater, R. F., Wightman, A. S.: PCT, spin and statistics and all that. New York: Benjamin 1964Google Scholar
  10. 6.
    Strocchi, F.: Phys. Rev.162, 1429 (1967);Google Scholar
  11. 6a.
    Strocchi, F., Wightman, A.S.: J. Math. Phys.15, 2198 (1974);Google Scholar
  12. 6b.
    Strocchi, F.: Local and covariant gauge quantum field theories; cluster property, superselection rules, and infrared problem. Invited talk at the Workshop on Quantum Electrodynamics, Aspen, June 1976Google Scholar
  13. 7.
    For a review see Coleman, S.: Secret symmetries, Erice (1973)Google Scholar
  14. 8.
    Ferrari, R.: Nuovo Cimento19A, 204 (1974)Google Scholar
  15. 9.
    See Coleman, S.: Lectures at the Erice Summer School (1973)Google Scholar
  16. 10.
    Strocchi, F.: Phys. Letters62B, 60 (1976)Google Scholar
  17. 11.
    Lowenstein, J., Swieca, J.: Ann. Phys. (N.Y.)68, 172 (1971);Google Scholar
  18. 11a.
    Casher, A., Kogut, J., Susskind, L.: Phys. Rev. Letters31, 792 (1973)Google Scholar
  19. 12.
    Strocchi, F., Wightman, A.S.: J. Math. Phys.15, 2198 (1974)Google Scholar
  20. 13.
    Gupta, S.: Proc. Phys. Soc. Lond. A63, 681 (1950);Google Scholar
  21. 13a.
    Bleuler, K.: Helv. Phys. Acta23, 567 (1950)Google Scholar
  22. 14.
    See e.g. Wightman, A. S.: Physics Today22, 53 (1969)Google Scholar
  23. 15.
    Strocchi, F.: Gauge groups in local field theory and superselection rules. In: Proceedings of the 4th International Colloquium on Group Theoretical Methods in Physics, Nijmegen June 1975. Lecture Notes in Physics, Vol. 50. Berlin-Heidelberg-New York: Springer 1976Google Scholar
  24. 16.
    Strocchi, F.: Local and covariant gauge quantum field theories; cluster property, superselection rules, and infrared problem. Invited talk at the Workshop on Quantum Electrodynamics, Aspen, June 1976Google Scholar
  25. 17.
    Bracci, L., Morchio, G., Strocchi, F.: Commun. math. Phys.41, 289 (1975)Google Scholar
  26. 18.
    Swieca, J.: Goldstone theorem and related topics. In: Cargèse lectures in physics, Vol. 4 (ed. D. Kastler), p. 215, Section III. New York: Gordon and Breach 1970Google Scholar
  27. 19.
    This fact has been remarked by several people. See Reeh, H.: Symmetries, currents and infinitesimal generators (Lectures at the International Seminar at Haifa, Israel, August 1971). In: Statistical mechanics and field theory. (Eds. R. N. Sen and C. Weil). Israel: University Press 1972Google Scholar
  28. 20.
    See e.g. Dothan, Y., Gal-Ezer, E.: Nuovo Cimento12A, 465 (1972);Google Scholar
  29. 20a.
    Ferrari, R.: Nuovo Cimento14A, 386 (1973), etc.Google Scholar
  30. 21.
    Reeh, H.: Fortschr. Physik16, 687 (1968)Google Scholar
  31. 22.
    Schwartz, L.: Théorie des Distributions, Chapter VIII, Section 5. Paris: Hermann 1966Google Scholar
  32. 23.
    Araki, H., Hepp, K., Ruelle, D.: Helv. Phys. Acta35, 164 (1962)Google Scholar
  33. 24.
    Wightman, A.S.: Analytic functions of several complex variables. In: Relations de dispersion et particules elémentaires. Les Houches Lectures 1960 (eds. C. De Witt and R. Omnes), Chapter VII. Paris: Hermann 1960Google Scholar
  34. 25.
    Ferrari, R., Picasso, L.E., Strocchi, F.: Commun. math. Phys.35, 25 (1974)Google Scholar
  35. 26.
    Swieca, J. A.: Phys. Rev. D13, 312 (1976)Google Scholar
  36. 27.
    Ferrari, R.: Nuovo Cimento19A, 204 (1974)Google Scholar
  37. 28.
    Doplicher, S., Haag, R., Roberts, J.: Commun. math. Phys.13, 1 (1969);15, 173 (1969);23, 199 (1971)Google Scholar
  38. 29.
    Callan, C., Dashen, R., Gross, D.: Phys. Letters63B, 334 (1976)Google Scholar
  39. 30.
    This case has been discussed in detail by Ferrari, R., Picasso, L. E.: Nucl. Phys. B31, 316 (1971), under the assumption [U(a), η]=0, in the case of QEDGoogle Scholar
  40. 31.
    Strocchi, F., Wightman, A.S.:Google Scholar
  41. 32.
    Schroer, B.: Fortschr. Phys.11, 1 (1963)Google Scholar
  42. 33.
    Buchholz, D.: To be publishedGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • F. Strocchi
    • 1
  1. 1.Joseph Henry Laboratories of PhysicsPrinceton UniversityPrincetonUSA

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