Perturbation Theory with a Variational Basis: the Generalized Gaussian Effective Potential

TL;DR

This paper develops a perturbation theory using a variational basis, introducing the generalized Gaussian effective potential, and analyzes its properties, renormalization, thermal effects, and symmetry restoration in scalar fields.

Contribution

It introduces and evaluates the generalized Gaussian effective potential up to second order, incorporating thermal corrections and analyzing symmetry restoration at high temperatures.

Findings

Generalized Gaussian effective potential evaluated up to second order.

Renormalization of mass discussed in detail.

Thermal corrections and symmetry restoration analyzed.

Abstract

The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial dimensions. The problem of the renormalization of the mass is discussed in details. Thermal corrections are incorporated. The comparison between the finite temperature generalized Gaussian effective potential and the finite temperature effective potential is critically analyzed. The phenomenon of the restoration at high temperature of the symmetry broken at zero temperature is discussed.