Dynamical symmetry breaking in QCD-like gauge theories

Abstract

We present an explicit derivation of an effective action for composite operators which has the same local extrema as the effective action of Cornwall, Jackiw and Tomboulis. Our effective action, which we have already used in a particular application, can be shown to reproduce in quadrilinear field theories the effective action obtained with the method of collective variables at one-loop level. It has the advantage of eliminating the problem of unboundness-below of the potential in the free case, and when applied to QCD-like theories at one-loop level, gives, with the theoretically suggested ansatz, only the local minima. We discuss different ansatz with or without logarithmic corrections in the coupling constant and in the fermion self-energy, and we find that the result of spontaneous breaking of chiral symmetry for large coupling remains stable.