Constraining fermionic condensates

TL;DR

This paper introduces a novel method to analyze spontaneous symmetry breaking in fermionic quantum field theories by constructing a constraint effective potential, validated in the Gross-Neveu model, with implications for understanding chiral symmetry in strong interactions.

Contribution

It develops the first construction of the constraint effective potential for fermionic order parameters using a large-volume expansion and saddle-point approximation.

Findings

Method is consistent with standard approaches in the Gross-Neveu model.

Enables new investigations into fermionic symmetry breaking and restoration.

Provides a framework for studying chiral symmetry breaking in strong interactions.

Abstract

We study spontaneous symmetry breaking in quantum field theories with fermionic order parameters and construct, for the first time in the literature, the constraint effective potential for it. The Grassmann-valued constraint we encounter is handled using its large-volume expansion, corresponding to a saddle-point approximation. We test the method in the chiral Gross-Neveu model and demonstrate its consistency with the standard approach. The machinery we developed opens up a new avenue to investigate the spontaneous symmetry breaking and restoration in field theories, in particular for the chiral symmetry breaking in the strong interactions.