Classification of generalized symmetries of the Yang-Mills fields with a semi-simple structure group

TL;DR

This paper classifies all generalized symmetries of Yang-Mills equations with semi-simple structure groups on Minkowski space, showing they are essentially gauge and conformal symmetries plus complex structure images.

Contribution

It provides a complete classification of generalized symmetries for Yang-Mills fields with semi-simple groups, identifying their structure up to gauge equivalence.

Findings

Any generalized symmetry matches a first order symmetry on solutions.

First order symmetries include gauge, conformal, and complex structure images.

Symmetries are classified according to the decomposition of the Lie algebra.

Abstract

A complete classification of generalized symmetries of the Yang-Mills equations on Minkowski space with a semi-simple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with a first order symmetry on solutions of the Yang-Mills equations. Let $g=g_1+...+g_n$ be the decomposition of the Lie algebra $g$ of the structure group into simple ideals. First order symmetries for $g$-valued Yang-Mills fields are found to consist of gauge symmetries, conformal symmetries for $g_m$-valued Yang-Mills fields, $1\leq m\leq n$, and their images under a complex structure of $g_m$.