An integral formulation of Yang-Mills on loop space

TL;DR

This paper introduces an integral approach to classical Yang-Mills equations using loop space concepts, enabling the construction of gauge-invariant conserved quantities and enhancing understanding of non-abelian gauge theories' global properties.

Contribution

It presents a novel integral formulation of Yang-Mills equations based on loop space and a generalized non-abelian Stokes theorem, emphasizing gauge invariance and parameterization independence.

Findings

Constructed gauge-invariant conserved quantities

Provided a new perspective on global properties of gauge theories

Extended the non-abelian Stokes theorem to loop space

Abstract

It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads in a quite direct way to the construction of gauge invariant conserved quantities which are also independent of the parameterization of surfaces and volumes. Our results are important in understanding global properties of non-abelian gauge theories.