Multisymplectic formulation of Yang--Mills equations and Ehresmann connections

TL;DR

This paper develops a multisymplectic framework for Yang--Mills equations, showing that equivariance of connections naturally emerges from the equations without prior assumptions.

Contribution

It introduces a multisymplectic formulation of Yang--Mills equations that relaxes the need for initial equivariance assumptions on connections.

Findings

Equivariance condition arises from the equations themselves.

Connections are represented by normalized equivariant 1-forms.

Multisymplectic approach provides new insights into gauge theories.

Abstract

We present a multisymplectic formulation of the Yang--Mills equations. The connections are represented by normalized equivariant 1-forms on the total space of a principal bundle, with values in a Lie algebra. Within the multisymplectic framework we realize that, under reasonable hypotheses, it is not necessary to assume the equivariance condition a priori, since this condition is a consequence of the dynamical equations.