From condensed matter to QCD: a journey through gauge theories on board of a variational tool

TL;DR

This paper reviews the Gaussian Effective Potential as a variational method for gauge theories, demonstrating its application to QCD, symmetry breaking, and gluon mass generation, bridging condensed matter and high-energy physics.

Contribution

It introduces a novel variational derivation of the massive expansion for QCD, linking it to the Gaussian Effective Potential and providing insights into chiral symmetry breaking.

Findings

Gaussian Effective Potential effectively studies symmetry breaking.

Variational proof of gluon mass generation.

New derivation of QCD massive expansion.

Abstract

Starting with a review of the thermal fluctuations in superconductors, the Gaussian Effective Potential is shown to be a powerful variational tool for the study of the breaking of symmetry in gauge theories. A novel re-derivation of the massive expansion for QCD is presented, showing its variational nature and its origin from the Gaussian potential that also provides a variational proof for chiral symmetry breaking and dynamical generation of a gluon mass.