Quantization of Non-Abelian Yang-Mills Theories

TL;DR

This paper explores the quantization of non-Abelian Yang-Mills theories with fermions, analyzing the system's equations of motion, integrability, and applying canonical quantization methods.

Contribution

It provides a detailed analysis of the equations of motion and demonstrates the quantization process using canonical methods for non-Abelian gauge theories.

Findings

Equations of motion are shown to be integrable.

Quantization is successfully performed via canonical methods.

The approach clarifies the phase space structure of the theory.

Abstract

A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions are investigated and the set of equations of motion is integrable. The Senjanovic and the canonical methods are used to quantize the system, and the integration is taken over the canonical phase space coordinates.