Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations

TL;DR

This paper extends Yang-Mills theory by incorporating nonlinear constitutive equations for non-Abelian gauge fields, exploring Lagrangian conditions, specific models like non-Abelian Born-Infeld, and analyzing Galilean limits.

Contribution

It introduces a generalized framework for Yang-Mills theories with nonlinear constitutive relations, including conditions for Lagrangian structure and explicit Galilean limit analysis.

Findings

Identified conditions for Lagrangian formulations of generalized theories

Derived explicit Galilean limits for certain models

Connected non-Abelian Born-Infeld theories within the new framework

Abstract

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.