The Yang-Mills field strength revisited

TL;DR

This paper provides a classical gauge theory derivation of the Yang-Mills field strength, highlighting its non-Abelian features and historical development, which has been overlooked in literature for over fifty years.

Contribution

It offers a heuristic derivation of the Yang-Mills field strength using classical gauge theory and clarifies historical and conceptual aspects of its development.

Findings

Derivation of Yang-Mills field strength from classical gauge theory

Historical analysis of Yang and Mills' original approach

Connection to Pauli's earlier expression for electromagnetic field strength

Abstract

The Yang-Mills field strength incorporating a non-Abelian feature is one of the cornerstones of the standard model. Although Yang-Mills gauge theories have been around for over fifty years, surprisingly the derivation of the Yang-Mills field strength using classical gauge theory does not appear anywhere in the literature. In their 1954 paper, Yang and Mills had to invent a non-Abelian field strength to satisfy certain criteria. In Section 5 we use Yang's gauge transformation in a heuristic derivation of the Yang-Mills field strength. The preceding sections cover material relating to the derivation. Section 3 shows where Pauli in the article cited by Yang and Mills gives an expression for the electro-magnetic field strength in terms of a commutator. For some reason, Yang and Mills did not use this approach.