Perturbative Expansion around the Gaussian Effective Potential of the Fermion Field Theory

TL;DR

This paper extends the perturbative expansion method around the Gaussian effective potential to fermionic field theories, specifically applying it to the 2D Gross-Neveu model to improve predictions of critical temperature for symmetry restoration.

Contribution

It introduces a perturbative approach around the Gaussian effective action for fermionic theories and applies it to the Gross-Neveu model, enhancing the accuracy of critical temperature calculations.

Findings

Improved estimate of critical temperature for small flavor numbers.

Effective potentials computed at zero and finite temperature.

Significant correction to symmetry restoration point.

Abstract

We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-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 small value of the flavour number.