Classical self-energy and anomaly

Abstract

We study the problem of self-energy of pointlike charges in higher dimensional static spacetimes. Their energy, as a functional of the spacetime metric, is invariant under a specific continuous transformation of the metric. We show that the procedure of regularization of this formally divergent functional breaks this symmetry and results in an anomalous contribution to the finite renormalized self-energy. We propose a method of calculation of this anomaly and present an explicit expression for it in the case of a scalar charge in four- and five-dimensional static spacetimes. This anomalous correction proves to be zero in even dimensions, but it does not vanish in odd-dimensional spacetimes.