Dynamical Symmetry Breaking on Langevin Equation : Nambu $\cdot$ Jona-Lasinio Model

TL;DR

This paper explores dynamical symmetry breaking in the Nambu-Jona-Lasinio model using stochastic quantization, constructing an effective Langevin equation that reproduces non-perturbative results and analyzing vacuum stability.

Contribution

It introduces a novel approach to study symmetry breaking via effective Langevin equations in the large-N limit, aligning with path-integral results.

Findings

Effective Langevin equation reproduces non-perturbative results.

Vacuum stability analyzed through effective potential.

Method provides a new perspective on dynamical symmetry breaking.

Abstract

In order to investigate dynamical symmetry breaking, we study Nambu$\cdot$Jona-Lasinio model in the large-N limit in the stochastic quantization method. Here in order to solve Langevin equation, we impose specified initial conditions and construct ``effective Langevin equation'' in the large-N limit and give the same non-perturbative results as path-integral approach gives. Moreover we discuss stability of vacuum by means of ``effective potential''.