Ultraviolet singularities in classical brane theory

TL;DR

This paper develops a Lorentz-invariant regularization method to construct a finite, unique energy-momentum tensor for electromagnetic fields of p-branes in any dimension, enabling consistent self-force calculations.

Contribution

It introduces a novel regularization and subtraction scheme to define a finite energy-momentum tensor for arbitrary-dimensional branes, ensuring energy-momentum conservation and finite self-force.

Findings

Constructed a finite energy-momentum tensor for p-branes.

Derived a finite self-force for moving branes.

Ensured energy-momentum conservation in the regularization process.

Abstract

We construct for the first time an energy-momentum tensor for the electromagnetic field of a p-brane in arbitrary dimensions, entailing finite energy-momentum integrals. The construction relies on distribution theory and is based on a Lorentz-invariant regularization, followed by the subtraction of divergent and finite counterterms supported on the brane. The resulting energy-momentum tensor turns out to be uniquely determined. We perform the construction explicitly for a generic flat brane. For a brane in arbitrary motion our approach provides a new paradigm for the derivation of the, otherwise divergent, self-force of the brane. The so derived self-force is automatically finite and guarantees, by construction, energy-momentum conservation.