# Gauge fixing problem and the constrained quantization

## TL;DR

This paper investigates the challenges of applying Dirac's canonical quantization to Yang-Mills theory using generalized Coulomb gauge, highlighting difficulties in the non-Abelian case compared to Abelian theories.

## Contribution

It analyzes the constraints in Yang-Mills theory and discusses the limitations of the canonical quantization method with Coulomb gauge for non-Abelian gauge fields.

## Key findings

- Successful quantization of Abelian theories
- Difficulties encountered in non-Abelian case
- Constraints matrix construction analyzed

## Abstract

In this work, the quantization of the Yang-Mills theory is worked out by means of Dirac's canonical quantization method, using the generalized Coulomb gauge fixing conditions. Following the construction of the matrix composed of all the second class constraints of the theory, its convenience within the framework of the canonical approach is discussed. Although this method can be used successfully in the quantization of the Abelian theories, it brings along difficulties for the non-Abelian case, which can not be handled easily even for the generalized Coulomb gauge of the Yang-Mills theory.