Comparison of alternative effective potentials for dynamical symmetry breaking

Abstract

Three formulations using effective potentials for dynamical symmetry breaking derived from different source terms are examined. The auxiliary-field method in which a bilocal composite field is introduced leads to an effective potential for which the lowest-energy candidate vacuum is a local minimum. Further the second derivatives of this potential can be interpreted as masses and their positivity is a necessary condition for the validity of the composite-field loop expansion. Other top- ics discussed include the use of functional \ensuremath{\delta} functions as an alternative to the Legendre transform, comparisons of potentials in the Gross-Neveu model, and comments on which formulations respect the Pauli principle.