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Spectral functions in mathematics and physics

Author: Klaus Kirsten
Publisher: Boca Raton : Fla. : Chapman & Hall/CRC, cop. 2002.
Edition/Format:   Print book : EnglishView all editions and formats

Deals with spectral analysis and geometry. This book describes some of the many applications in physics, particularly to heat asymptotics, quantum field theory, statistical mechanics, the theory of  Read more...


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Document Type: Book
All Authors / Contributors: Klaus Kirsten
ISBN: 158488259X 9781584882596
OCLC Number: 470148019
Notes: Notes bibliogr. p. [357]-376. Index.
Description: 382 p. : ill. ; 25 cm
Contents: INTRODUCTIONA FIRST LOOK AT ZETA FUNCTIONS AND HEAT TRACESZeta Function in Quantum Field TheoryStatistical Mechanics of Finite Systems: Bose-Einstein CondensationLocal versus Global Boundary ConditionsZETA FUNCTIONS ON GENERALIZED CONES AND RELATED MANIFOLDSScalar Field on the Three-Dimensional BallScalar Field on the D-Dimensional Generalized ConeSpinor Field with Global and Local Boundary ConditionsForms with Absolute and Relative Boundary ConditionsOblique Boundary Conditions on the Generalized ConeFurther Examples on a Related GeometryCALCULATION OF HEAT KERNEL COEFFCIENTS VIA SPECIAL CASESHeat Equation Asymptotics for Manifolds without BoundaryGeneral Form for Dirichlet and Robin Boundary ConditionsHeat Kernel Coefficients on the Generalized ConeDetermination of the General Heat Kernel CoefficientsMixed Boundary ConditionsSpecial Case Calculations for Mixed Boundary ConditionsDetermination of the Mixed Heat Kernel CoefficientsOblique Boundary ConditionsLeading Heat Equation Asymptotics with Spectral Boundary ConditionsSummary of the ResultsFurther Boundary ConditionsHEAT CONTENT ASYMPTOTICSGeneral Form of the Heat Content CoefficientsDirichlet Boundary ConditionsRobin Boundary ConditionsHeat Content Asymptotics on the Generalized ConeMixed Boundary ConditionsFUNCTIONAL DETERMINANTSSome One-Dimensional ExamplesScalar FieldSpinor Field with Global and Local Boundary ConditionsForms with Absolute and Relative Boundary ConditionsDeterminants by Conformal TransformationCASIMIR ENERGIESScalar FieldSpinor Field with Global and Local Boundary ConditionsElectromagnetic Field with and without MediumMassive Scalar FieldMassive Spinor Field with Local Boundary ConditionsGROUND STATE ENERGIES UNDER THE INFLUENCE OF EXTERNAL FIELDSFormalism: Scattering Theory and Ground State EnergyExamples and General ResultsSpinor Field in the Background of a Finite Radius Flux TubeBOSE-EINSTEIN CONDENSATION OF IDEAL BOSE GASES UNDER EXTERNAL CONDITIONSIdeal Bose Gases in the Grand Canonical DescriptionCanonical Description of Ideal Bose-Einstein CondensatesMicrocanonical Condensate FluctuationsCONCLUSIONSAPPENDICESBasic Zeta FunctionsConformal Relations between Geometric TensorsApplication of Index TheoremsRepresentations for the Asymptotic ContributionsPerturbation Theory for the Logarithm of the Jost FunctionREFERENCESINDEX Each chapter also includes an Introduction and Concluding Remarks section
Responsibility: Klaus Kirsten.
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"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 Read more...

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