Lectures on quantization of gauge systems

TL;DR

This paper provides an overview of the path integral quantization method for gauge systems, focusing on classical theories with gauge invariance, exemplified by Yang-Mills and Chern-Simons theories.

Contribution

It offers a detailed exposition of quantization techniques specifically applied to gauge systems, highlighting the role of connections and gauge invariance.

Findings

Path integral quantization applied to gauge theories

Analysis of Yang-Mills and Chern-Simons models

Clarification of gauge invariance in quantization

Abstract

A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either invariant or transforms appropriately with respect to the action of the gauge group. The lectures are focused on the path integral quantization of such systems. Here two main examples of gauge systems are Yang-Mills and Chern-Simons.