Zeitschrift für Physik C Particles and Fields

, Volume 69, Issue 1, pp 359–363 | Cite as

Goldstone theorem in the Gaussian functional approximation to the scalarφ 4 theory

  • V. Dmitrašinović
  • J. A. McNeil
  • J. R. Shepard


We verify the Goldstone theorem in the Gaussian functional approximation to theφ 4 theory with internalO(2) symmetry. We do so by reformulating the Gaussian approximation in terms of Schwinger-Dyson equations from which an explicit demonstration of the Goldstone theorem follows directly. Axial current conservation is also shown to hold.


Feynman Diagram Gaussian Approximation Goldstone Boson Spontaneous Symmetry Breaking Linear Sigma Model 


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  1. 1.
    T. Barnes, G.I. Ghandour: Phys. Rev. D22 (1980) 924ADSGoogle Scholar
  2. 2.
    J.M. Cornwall, R. Jackiw, E. Tomboulis: Phys. Rev. D10 (1974) 2428ADSGoogle Scholar
  3. 3.
    P.M. Stevenson: Phys. Rev. D32 (1985) 1389; see also references in R. Ibañez-Meier, A. Mattingly, U. Ritschel, P.M. Stevenson: Phys. Rev. D45 (1992) 2893ADSGoogle Scholar
  4. 4.
    M. Consoli, A Ciancitto: Nucl. Phys. B254 (1985) 653CrossRefADSGoogle Scholar
  5. 5.
    A. Fetter, J.D. Walecka: Quantum Theory of Many-Body Systems. New York: McGraw-Hill 1971Google Scholar
  6. 6.
    J. Goldstone: Nuov. Cim. 19 (1961) 154MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Y. Brihaye, M. Consoli: Phys. Lett. B157 (1985) 48ADSGoogle Scholar
  8. 8.
    Y. Nambu, G. Jona-Lasinio: Phys. Rev. 122 (1961) 345CrossRefADSGoogle Scholar
  9. 9.
    R.J. Rivers: Path Integral Methods in Quantum Field Theory. Cambridge: Cambridge University Press 1987MATHGoogle Scholar
  10. 10.
    B.W. Lee: Chiral Dynamics. New York: Gordon and Breach 1972Google Scholar
  11. 11.
    B. Rosenstein, A. Kovner: p. 143 in eds. L. Polley, D.E.L. Pottinger: Variational Calculations in Quantum Field Theory. Singapore: World Scientific 1987Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • V. Dmitrašinović
    • 1
  • J. A. McNeil
    • 2
  • J. R. Shepard
    • 1
  1. 1.Nuclear Physics Laboratory, Physics DepartmentUniversity of ColoradoBoulderUSA
  2. 2.Physics DepartmentColorado School of MinesGoldenUSA

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