Anomaly and the self-energy of electric charges

TL;DR

This paper investigates the self energy of electric charges in static higher-dimensional gravitational fields, revealing gauge invariance, anomalies, and explicit calculations in specific spacetimes, linking classical self energy to quantum fluctuations.

Contribution

It introduces a gauge-invariant framework for calculating self energy of charges in D-dimensional gravity and connects it to quantum field fluctuations, with explicit anomaly computations.

Findings

Self energy functional is gauge invariant under an infinite-dimensional group.

Self energy calculation reduces to quantum fluctuations in an effective field theory.

Explicit anomalies in self energy are computed for higher-dimensional Majumdar-Papapetrou spacetimes.

Abstract

We study the self energy of a charged particle located in a static D-dimensional gravitational field. We show that the energy functional for this problem is invariant under an infinite dimensional (gauge) group of transformations parameterized by one scalar function of (D-1)-variables. We demonstrate that the problem of the calculation of the self energy for a pointlike charge is equivalent to the calculation of the fluctuations $<\psi^2>$ for an effective (D-1)-dimensional Euclidean quantum field theory. Using point-splitting regularization we obtain an expression for the self energy and show, that it possesses anomalies. Explicit calculation of the self energy and its anomaly is done for the higher dimensional Majumdar-Papapetrou spacetimes.