%0 Journal Article
%T Spectral functions in mathematics and physics
%A Klaus Kirsten
%J Physics
%D 2000
%I arXiv
%R 10.1063/1.59656
%X Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of Casimir energies. First, we summarize that a convenient way of handling them is to use the associated zeta function. A way to determine all its needed properties is derived. Using the connection with the mentioned spectral functions, we provide: i.) a method for the calculation of heat-kernel coefficients of Laplace-like operators on Riemannian manifolds with smooth boundaries and ii.) an analysis of vacuum energies in the presence of spherically symmetric boundaries and external background potentials.
%U http://arxiv.org/abs/hep-th/0005133v1