Overview
The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new, innovative methods for the exact analysis of a variety of spectral functions occurring in spectral geometry and under external conditions in statistical mechanics and quantum field theory. Spectral Functions in Mathematics and Physics presents a detailed overview of these advances. The author develops and applies methods for analyzing determinants arising when the external conditions originate from the Casimir effect, dielectric media, scalar backgrounds, and magnetic backgrounds. The zeta function underlies all of these techniques, and the book begins by deriving its basic properties and relations to the spectral functions. The author then uses those relations to develop and apply methods for calculating heat kernel coefficients, functional determinants, and Casimir energies. He also explores applications in the non-relativistic context, in particular applying the techniques to the Bose-Einstein condensation of an ideal Bose gas.Self-contained and clearly written, Spectral Functions in Mathematics and Physics offers a unique opportunity to acquire valuable new techniques, use them in a variety of applications, and be inspired to make further advances.
Full Product Details
Author: Klaus Kirsten
Publisher: Taylor & Francis Inc
Imprint: Chapman & Hall/CRC
Dimensions:
Width: 15.60cm
, Height: 2.70cm
, Length: 23.40cm
Weight: 0.890kg
ISBN: 9781584882596
ISBN 10: 158488259
Pages: 396
Publication Date: 13 December 2001
Audience:
College/higher education
,
General/trade
,
Postgraduate, Research & Scholarly
,
General
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
Spectral geometry and spectral analysis play an important role not only in global analysis but also in certain other areas of mathematics and physics. The book Spectral Functions in Mathematics and Physics is suitable for a wide audience of both experts and non experts in these fields--it is a well-written introduction to the field by one of the experts ... [it] will be useful to both mathematicians and mathematical physicists. - SIAM Review, 2003
""Spectral geometry and spectral analysis play an important role not only in global analysis but also in certain other areas of mathematics and physics. The book Spectral Functions in Mathematics and Physics is suitable for a wide audience of both experts and non experts in these fields--it is a well-written introduction to the field by one of the experts ... [it] will be useful to both mathematicians and mathematical physicists."" - SIAM Review, 2003
Author Information
Klaus Kirsten is a post-doctoral associate at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
