Gaussian-effective-potential studies of fermion-scalar theories

Abstract

We study some rather general 1+1 dimensional fermion-scalar models containing fourfermion terms, using the Gaussian-effective-potential (GEP) approach. Model I has a Yukawa\(\left( {\phi \bar \psi \psi } \right)\) coupling, and possesses a continuous chiral symmetry. Model II has a\(\phi ^2 \bar \psi \psi \) coupling, preserving theO(N) symmetry of the scalar sector. For each model two distinct kinds of renormalization are possible: in “case A” the fermion-scalar and four-fermion bare coupling constants may remain finite; in “case B” the bare couplings take on particular infinitesimal forms. For model I, the chiral symmetry is unbroken in case A, but spontaneously broken in case B. There are parallels with GEP studies of (λφ4)4 theory, where two distinct renormalizations (“autonomous” and “precarious”) are also found.