Yang-Mills and Beyond

TL;DR

This paper explores the historical development and theoretical foundations of Yang-Mills theory, explaining its derivation from gauge transformations and its role in the Standard Model of particle physics.

Contribution

It provides a detailed derivation of the Yang-Mills field strength from gauge transformations and contextualizes its significance in the evolution of particle physics theories.

Findings

Derivation of Yang-Mills field strength from gauge transformations

Historical perspective on Yang-Mills theory development

Connection of Yang-Mills theory with the Standard Model

Abstract

In their 1954 paper, Yang and Mills invented the non-Abelian field strength to satisfy certain criteria but didn't explain how it could be derived. In the penultimate section we show how the Yang-Mills field strength derives from Yang's gauge transformation. The preceding sections place Yang-Mills theory in historical perspective and cover material relating to the field strength. The final section shows how Yang-Mills theory was combined with spontaneous symmetry breaking, the Goldstone theorem and subsequent work to contribute to the Standard Model of particle physics.