Variational Approach to the Chiral Phase Transition in the Linear Sigma Model

TL;DR

This paper investigates the chiral phase transition in the linear sigma model at finite temperature using a variational Gaussian approach, highlighting the importance of momentum cutoff effects.

Contribution

It introduces a variational Gaussian method to study the chiral transition, ensuring Goldstone theorem compliance and incorporating meson excitations.

Findings

Goldstone theorem is preserved in the approach

Meson pair excitations are naturally included

Chiral transition behavior depends on momentum cutoff

Abstract

The chiral phase transition at finite temperature is investigated in the linear sigma model, which is regarded as a low energy effective theory of QCD with three momentum cutoff, in the variational method with the Gaussian approximation in the functional Schroedinger picture. It is shown that the Goldstone theorem is retained and the meson pair excitations are automatically included by taking into account the linear response to the external fields. It is pointed out that the behavior of chiral phase transition depends on the three-momentum cutoff, which leads to the careful treatment of the problem.