Characteristic Lightcone Sources in SO(1,3) Yang-Mills Theory

Abstract

The SO(1,3)-symmetric reduction of Yang-Mills theory on Minkowski space yields a stress-energy tensor that is smooth on the timelike and spacelike Lorentz orbits but diverges on the lightcone that separates the two regions. We ask what consistent source this singularity represents. A natural cure is a real shift of the singular denominator. This does not regularize the source but instead moves the singular support onto a hyperboloid off the cone, where the corresponding source cannot remain both conserved and traceless. Our analysis shows that the displaced support cannot retain both properties, whereas a completion on the lightcone can. The matching condition fixes this completion up to one parameter $\chi$, which has a causal interpretation as the relative weight of the future and past cones. On regular constant-time slices, the completed source carries zero total four-momentum, so its physical content is a residual causal charge inferred from its curvature response.

5 pages, 1 figure; v2: characteristic collar interpretation and improvement as double divergence added, matching published version

References in corpus (6)

• The Energy-Momentum Tensor(s) in Classical Gauge Theories
• Sphalerons and Conformally Compactified Minkowski Spacetime
• Solutions to Yang-Mills equations on four-dimensional de Sitter space
• Finite-action solutions of Yang-Mills equations on de Sitter dS${}_4$ and anti-de Sitter AdS${}_4$ spaces
• Yang-Mills solutions on de Sitter space of any dimension
• Yang-Mills solutions on Minkowski space via non-compact coset spaces