  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.
