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Spectral Functions in Mathematics and Physics

Spectral Functions in Mathematics and Physics by Klaus Kirsten
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INTRODUCTION
A FIRST LOOK AT ZETA FUNCTIONS AND HEAT TRACES
Zeta Function in Quantum Field Theory
Statistical Mechanics of Finite Systems: Bose-Einstein Condensation
Local versus Global Boundary Conditions
ZETA FUNCTIONS ON GENERALIZED CONES AND RELATED MANIFOLDS
Scalar Field on the Three-Dimensional Ball
Scalar Field on the D-Dimensional Generalized Cone
Spinor Field with Global and Local Boundary Conditions
Forms with Absolute and Relative Boundary Conditions
Oblique Boundary Conditions on the Generalized Cone
Further Examples on a Related Geometry
CALCULATION OF HEAT KERNEL COEFFCIENTS VIA SPECIAL CASES
Heat Equation Asymptotics for Manifolds without Boundary
General Form for Dirichlet and Robin Boundary Conditions
Heat Kernel Coefficients on the Generalized Cone
Determination of the General Heat Kernel Coefficients
Mixed Boundary Conditions
Special Case Calculations for Mixed Boundary Conditions
Determination of the Mixed Heat Kernel Coefficients
Oblique Boundary Conditions
Leading Heat Equation Asymptotics with Spectral Boundary Conditions
Summary of the Results
Further Boundary Conditions
HEAT CONTENT ASYMPTOTICS
General Form of the Heat Content Coefficients
Dirichlet Boundary Conditions
Robin Boundary Conditions
Heat Content Asymptotics on the Generalized Cone
Mixed Boundary Conditions
FUNCTIONAL DETERMINANTS
Some One-Dimensional Examples
Scalar Field
Spinor Field with Global and Local Boundary Conditions
Forms with Absolute and Relative Boundary Conditions
Determinants by Conformal Transformation
CASIMIR ENERGIES
Scalar Field
Spinor Field with Global and Local Boundary Conditions
Electromagnetic Field with and without Medium
Massive Scalar Field
Massive Spinor Field with Local Boundary Conditions
GROUND STATE ENERGIES UNDER THE INFLUENCE OF EXTERNAL FIELDS
Formalism: Scattering Theory and Ground State Energy
Examples and General Results
Spinor Field in the Background of a Finite Radius Flux Tube
BOSE-EINSTEIN CONDENSATION OF IDEAL BOSE GASES UNDER EXTERNAL CONDITIONS
Ideal Bose Gases in the Grand Canonical Description
Canonical Description of Ideal Bose-Einstein Condensates
Microcanonical Condensate Fluctuations
CONCLUSIONS
APPENDICES
Basic Zeta Functions
Conformal Relations between Geometric Tensors
Application of Index Theorems
Representations for the Asymptotic Contributions
Perturbation Theory for the Logarithm of the Jost Function
REFERENCES
INDEX
Each chapter also includes an Introduction and Concluding Remarks section
CRC Press; December 2001
397 pages; ISBN 9781420035469
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Title: Spectral Functions in Mathematics and Physics
Author: Klaus Kirsten
 
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