Perturbative expansion around the Gaussian effective potential of the fermion field theory

Abstract

We have extended the perturbative expansion method around the Gaussian effective action to fermionic field theory, by taking the two-dimensional Gross-Neveu model as an example. We have computed both the zero-temperature and the finite-temperature effective potentials of the Gross-Neveu model up to the first perturbative correction terms, and have found that the critical temperature, at which dynamically broken symmetry is restored, is significantly improved for the small value of the flavor number.