Group theory of the effective potential

  • W. Lang
  • L. O'Raifeartaigh
  • G. Parravicini
Atomic, molecular, solid-State, and statistical physics
Part of the Lecture Notes in Physics book series (LNP, volume 135)


A simple group theoretical proof is given of the result that, to all orders of perturbation, the effective potential in scalar quantum field theory can be expressed as an expansion of the vacuum graphs. Although, this result has been established for some time we have felt it worthwhile to present our proof for a number of reasons. First, the result though not new, does not appear to be as well-;sown as it deserves. Second, the proof follows immediately from d very simple group-theoretical consideration and is much simpler than its forerunners. Third, the proof establishes a one-one correspondence between the convexity of the classical potential and the reality of the effective potential (thus clarifying the appearance of complex values for some effective potentials, notably in the case of spontaneous symmetry breakdown). Finally, a general relationship between the classical field and the quantum mechanical mean field is found as a bye-product.


Effective Action Effective Potential Radiative Correction Classical Limit Classical Field 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • W. Lang
    • 1
  • L. O'Raifeartaigh
    • 2
  • G. Parravicini
    • 3
  1. 1.Max Planck InstituteMünchen 40Germany
  2. 2.Dublin Institute for Advanced StudiesDublin 4Ireland
  3. 3.Institute of Theoretical PhysicsUniversity of MilanMilanItaly

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