Classical self-energy and anomaly

TL;DR

This paper investigates the self-energy of point charges in higher-dimensional static spacetimes, revealing an anomaly in the regularization process that affects the finite self-energy, especially in odd dimensions.

Contribution

It introduces a method to calculate the self-energy anomaly in higher dimensions and provides explicit formulas for scalar charges in four and five dimensions.

Findings

Anomaly vanishes in even dimensions

Anomaly is non-zero in odd dimensions

Regularization breaks the symmetry of the self-energy functional

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 proposed a method of calculation of this anomaly and presented an explicit expressions 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.