Spectral functions in mathematics and physics
摘要
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.
引用
@article{arxiv.hep-th/0005133,
title = {Spectral functions in mathematics and physics},
author = {Klaus Kirsten},
journal= {arXiv preprint arXiv:hep-th/0005133},
year = {2015}
}
备注
51 pages, Invited talk at 2nd La Plata Meeting on Trends in Theoretical Physics, Buenos Aires, Argentina, November-December 1998, Published in AIP Conference Proceedings 484, page 106, Edited by H. Falomir, R.E. Gamboa Saravi and F.A. Schaposnik