Spectral functions in mathematics and physics

Details Spectral functions in mathematics and physics Spectral functions in mathematics and physics

2000-05-15

arxiv.org/abs/hep-th/0005133v1

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, Invited talk at 2nd La Plata Meeting on Trends in Theoretical Physics, Buenos Aires, Argentina, November-December 19

Scientific paper

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.

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