Spectral Functions in Mathematics and Physics - Softcover

Kirsten, Klaus

Softcover

ISBN 10: 0367455064 ISBN 13: 9780367455064

Publisher: Routledge, 2019

Synopsis

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.

About this title

About the Author

Klaus Kirsten is a post-doctoral associate at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.

From the Back Cover

Over the last several years, the author and his colleagues have developed new methods for the exact analysis of different spectral functions that are significant in physics. This book provides a comprehensive description of these techniques and their various applications. The author's approach allows for an exact treatment of zeta functions associa

Edition details

• Publisher: Routledge
• Publication date: 2019
• Language: English
• ISBN 10: 0367455064
• ISBN 13: 9780367455064
• Binding: Paperback
• Edition number: 1
• Number of pages: 400