Decomposing the SU(N) Connection and the Wu-Yang Potential

TL;DR

This paper generalizes the decomposition of SU(2) gauge fields to SU(N), deriving invariant electromagnetic tensors and Wu-Yang potentials, and discusses sourceless solutions in non-Abelian gauge theories.

Contribution

It extends the SU(2) gauge field decomposition framework to SU(N), providing new invariant tensors and potentials for broader gauge group applications.

Findings

Derived a generalized decomposition theory for SU(N) gauge fields

Obtained invariant electromagnetic tensors for SU(N) groups

Discussed sourceless solutions in the extended framework

Abstract

Based on the decomposition of SU(2) gauge field, we derive a generalization of the decomposition theory for the SU(N) gauge field. We thus obtain the invariant electro-magnetic tensors of SU(N) groups and the extended Wu-Yang potentials. The sourceless solutions are also discussed.