Spectral Functions in Mathematics and Physics

Klaus Kirsten

382 pages, parution le 07/03/2002

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Résumé

Over the last several years, the author and his colleagues have developed new methods for the exact analysis, including numerical evaluations, of different spectral functions that have significant applications in physics. This book provides a comprehensive description of these techniques and of their various applications. The approach allows for an exact treatment of zeta functions associated with the spectrum of a certain class of second order elliptic differential operators. Although much of the book is devoted to spectral analysis and spectral geometry, it also demonstrates some of the many ramifications spectral analysis and geometry has in physics, particularly to heat asymptotics, quantum field theory, statistical mechanics, the theory of partitions, and Bose-Einstein condensation.

Contents

1 Introduction 1
2 A first look at zeta functions and heat traces 9
3 Zeta functions on generalized cones and related manifolds 41
4 Calculation of heat kernel coefficients via special cases 87
5 Heat content asymptotics 181
6 Functional determinants 199
7 Casimir energies 229
8 Ground-state energies under the influence of external fields 255
9 Bose-Einstein condensation of ideal Bose gases under external conditions 289
10 Conclusions 307

A Basic zeta functions 313
B Conformal relations between geometric tensors 321
C Application of index theorems 333
D Representations for the asymptotic contributions 339
E Perturbation theory for the logarithm of the Jost function 349

References 357
Index 377

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Klaus Kirsten
Parution	07/03/2002
Nb. de pages	382
Format	16 x 24
Couverture	Broché
Poids	723g
Intérieur	Noir et Blanc
EAN13	9781584882596
ISBN13	978-1-58488-259-6