Il Nuovo Cimento A (1965-1970)

, Volume 109, Issue 8, pp 1187–1196 | Cite as

Higgs mechanism in the Gaussian functional approximation

  • V. Dmitraŝinović


The Higgs mechanism is explicity verified and its gauge invariance confirmed in the Gaussian ground-state functional approximation to theO(2) symmetric ϕ4 theory coupled to an Abelian gauge field. We demonstrate this by using the recent proof of the Goldstone theorem in the said approximation and the Englert-Brout-Schwinger method. The mass of the vector gauge boson is evaluated and expressed in terms of the dressed properties of the scalar fields and the gauge field coupling constant.


11.15.Ex Spontaneous breaking of gauge symmetries 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Higgs P. W.,Phys. Lett.,12 (1964) 132;Phys. Rev. Lett.,13 (1964) 508;Phys. Rev.,145 (1966) 1156.CrossRefADSGoogle Scholar
  2. [2]
    Englert F. andBrout R.,Phys. Rev. Lett.,13 (1964) 321.MathSciNetCrossRefADSGoogle Scholar
  3. [3]
    Guralnik G. S., Hagen C. R. andKibble T. W. B.,Phys. Rev. Lett.,13 (1964) 585.CrossRefADSGoogle Scholar
  4. [4]
    For an original reference, seeBarnes T. andGhandour G. I.,Phys. Rev. D,22 (1980) 924; for proceedings of an international workshop, seePolley L. andPottinger D. E. L. (Editors),Variational Calculations in Quantum Field Theory (World Scientific, Singapore) 1987; for a clear introduction to functional methods and the Gaussian approximation in particular, seeHatfield B.,Quantum Field Theory of Point Particles and Strings (Addison Wesley, Reading) 1992; for an equivalent variational approach, termed Hartree-type approximation, that does not use functional methods, seeChang S-J.,Phys. Rev. D,12 (1975) 1071; for the largeN limit of the ϕ4 model within such a “mean-field” or “RPA” approach, seeBender C. M., Cooper F. andGuralnik G. S.,Ann. Phys.,109 (1977) 165.CrossRefADSGoogle Scholar
  5. [5]
    Ibañez-Meier R., Stancu I. andStevenson P. M.,Z. Phys. C,70 (1996) 307; for a related approach, with similar problems, to non-Abelian gauge theories in the largeN limit seeKang J. S.,Phys. Rev. D,14 (1976) 1587.CrossRefGoogle Scholar
  6. [6]
    Schwinger J.,Phys. Rev.,125 (1962) 397;128 (1962) 2425.MathSciNetCrossRefADSMATHGoogle Scholar
  7. [7]
    V. Dmitraŝinović, McNeil J. A. andShepard J.,Z. Phys. C,69 (1996) 359.CrossRefGoogle Scholar
  8. [8]
    Abers E. S. andLee B. W.,Phys. Rep. C,9 (1973) 1.CrossRefADSGoogle Scholar
  9. [9]
    Rivers R. J.,Path Integral Methods in Quantum Field Theory (Cambridge University Press, Cambridge) 1987.CrossRefGoogle Scholar
  10. [10]
    Lee B. W.,Nucl. Phys. B,9 (1969) 649.CrossRefADSGoogle Scholar
  11. [11]
    Lee B. W.,Chiral Dynamics (Gordon and Breach, New York, N.Y.) 1972.Google Scholar
  12. [12]
    Brihaye Y. andConsoli M.,Phys. Lett. B,157 (1985) 48.CrossRefADSGoogle Scholar
  13. [13]
    Itzykson C. andZuber J.-B.,Quantum Field Theory (McGraw-Hill, New York, N.Y.) 1980.Google Scholar
  14. [14]
    Gherghetta T.,Phys. Rev. D,50 (1994) 5985.CrossRefADSGoogle Scholar
  15. [15]
    Bardeen W. A. andMoshe M.,Phys. Rev. D,28 (1983) 1372;Stevenson P. M.,Phys. Rev. D,32 (1985) 1389.CrossRefADSGoogle Scholar
  16. [16]
    Stevenson P. M. andTarrach R.,Phys. Lett. B,176 (1986) 436;Stevenson P. M.,Z. Phys. C,35 (1987) 467.MathSciNetCrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1996

Authors and Affiliations

  • V. Dmitraŝinović
    • 1
  1. 1.Nuclear Physics Laboratory, Physics DepartmentUniversity of ColoradoBoulderUSA

Personalised recommendations