Investigation of spontaneous symmetry breaking from a non standard approach

TL;DR

This paper introduces a novel method for analyzing spontaneous symmetry breaking in quantum field theories by computing the probability distribution function of the chiral condensate, avoiding the need for external symmetry-breaking fields.

Contribution

It presents a new approach based on probability distribution functions to study chiral properties in QFTs, circumventing the limitations of simulating Grassmann variables.

Findings

Method enables analysis without external symmetry-breaking fields

Applicable to fermionic quantum field theories

Provides insights into chiral symmetry breaking mechanisms

Abstract

We propose a new method for the study of the chiral properties of the ground state in Quantum Field Theories (QFT's) which is based on the computation of the probability distribution function (p.d.f.) of the chiral condensate in the chiral limit. We show how despite of the fact that Grassmann variables cannot be simulated on a computer, an analysis of spontaneous symmetry breaking without a symmetry breaking external field, which is standard in the case of spin systems, can also be done in QFT's with fermion degrees of freedom.