SO(1,3) Yang-Mills solutions on Minkowski space via cosets

TL;DR

This paper constructs new SO(1,3) Yang-Mills solutions on Minkowski space, distinguishing interior and exterior lightcone regions through coset foliations, and discusses their regularization despite divergence at the lightcone.

Contribution

It introduces a novel family of SO(1,3) Yang-Mills solutions on Minkowski space using coset foliations, with a method to regularize their stress-energy tensor.

Findings

Solutions are divided into interior and exterior lightcone classes.

Stress-energy tensor diverges at the lightcone but can be regularized.

Analytic solutions are obtained for an SO(1,3)-invariant gauge field.

Abstract

We present a novel family of Yang-Mills solutions, with gauge group SO(1,3), on Minkowski space that are geometrically distinguished into two classes, viz. interior and exterior of the lightcone. We achieve this by foliating the former with SO(1,3)/SO(3) cosets and the latter with SO(1,3)/SO(1,2) cosets and analytically solving the Yang-Mills equation of an SO(1,3)-invariant gauge field. The resulting fields and their stress-energy tensor, when translated to the Minkowski space, diverge at the lightcone, but we demonstrate how this stress-energy tensor could be regularised due to its unique algebraic structure.