Gauge fixing and BRST formalism in non-Abelian gauge theories

TL;DR

This thesis explores gauge fixing and BRST formalism in non-Abelian gauge theories, proposing new methods for quantization and addressing challenges like the Neuberger no-go theorem in lattice Yang-Mills theory.

Contribution

It introduces a group-theoretical approach to Faddeev-Popov quantization and proposes a solution to the Neuberger no-go theorem for lattice gauge theories.

Findings

Reformulation of Faddeev-Popov method using group theory

Proposed solution to Neuberger no-go theorem

Analysis of Batalin-Vilkovisky quantization in non-linear gauges

Abstract

In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of group-theoretical techniques and then we give a possible way to solve the no-go theorem of Neuberger for lattice Yang-Mills theory with double BRST symmetry. In the final part we present a study of the Batalin-Vilkovisky quantisation method for non-linear gauges in non-Abelian gauge theories.