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

Ultraviolet singularities in classical brane theory