Spectral Functions in Mathematics and Physics
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A01=Klaus Kirsten
Adjoint Boundary Condition
advanced mathematical techniques
Atiyah Singer Index Theorem
Author_Klaus Kirsten
Barnes zeta functions
Bose Einstein Condensation
boundary
casimir
Casimir Energy
Category=PBM
Category=PBW
Category=PHU
Category=PSA
coefficient
Compact Smooth Riemannian Manifolds
condition
Contour Integral Representation
Dirichlet Boundary Conditions
Elliptic Differential Operator
elliptic operator theory
energy
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
external field effects
Extrinsic Curvature
functional determinant calculation
Global Boundary Conditions
Grand Canonical
Grand Canonical Partition Function
Harmonic Oscillator Potential
heat
Heat Kernel Coefficients
Heat Trace
Ideal Bose Gas
kernel
mathematical physics
Ordinary Differential Equation
Partition Sum
Pseudo-differential Calculus
Pseudo-differential Operator
Quantum Field Theory
quantum statistical mechanics
robin
Robin Boundary Conditions
Spec Trum
Special Case Calculation
spectral analysis methods
spectral functions
spectral geometry applications in physics
spinor
Time Dependent Heat Source
zeta
Product details
- ISBN 9780367455064
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 25 Nov 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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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.
Klaus Kirsten is a post-doctoral associate at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
