On SU(2) Yang-Mills Theory and the Maximal Abelian Gauge

TL;DR

This paper investigates the degrees of freedom in SU(2) gauge theories, demonstrating that classical pure SU(2) theory is equivalent to an abelian theory and that the Maximal Abelian Gauge correctly isolates these abelian degrees of freedom.

Contribution

It proves that the Maximal Abelian Gauge accurately identifies the abelian degrees of freedom in SU(2) gauge theories, clarifying the gauge's role in the theory's dynamics.

Findings

Classical pure SU(2) gauge theory is equivalent to an abelian theory.

The Maximal Abelian Gauge correctly isolates abelian degrees of freedom.

The study extends to SU(N) theories, providing broader insights.

Abstract

The problem of identifying the dynamical degrees of freedom for SU(2) gauge theories is discussed. After studying SU(N) theories, it is shown that classical pure SU(2) gauge theory is equivalent to an abelian theory. Finally, we prove that the Maximal Abelian Gauge correctly identifies the abelian degrees of freedom of the SU(2) theory.