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

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.

7 pages, 2 figures; proceeding submission based on an in-person talk delivered at the 34th International Colloquium on Group Theoretical Methods in Physics at Strasbourg, 18-22 July 2022