最 低 价：￥621.40
定 价：￥731.00
作 者：Andrei A. Bytsenko 著 著
出 版 社：Pengiun Group (USA)
出版时间：2003-12-1
I S B N：9789812383648
| Chapter 1 Survey of Path Integral Quantization and Regu- larization Techniques 1.1 Path Integral and Regularization Techniques for Functional De-terminants 1.2 Schwinger-Like Regularizations and Heat-Kernel Expansion 1.3 Logarithmic Terms in the Heat-Kernel Expansion 1.4 One-Loop Renormalization Group Equations 1.5 Static Spacetimes: Thermodynamic Effects 1.5.1 Static and ultrastatic spacetimes 1.5.2 Finite-temperature effects 1.5.3 The free energy 1.5.4 The thermodynamic potential 1.5.5 Regularization of the vacuum energy 1.5.6 A generalized vacuum energy formula Chapter 2 The Zeta-Function Regularization Method 2.1 Survey of the Chapter, Notation and Conventions 2.1.1 Feasibility of physical interpretation via Wick rotation 2.1.2 Notation and general hypotheses 2.2 Heat-Kernel Expansion and Coefficients 2.2.1 The heat-kernel expansion on compact manifolds 2.2.2 The self-adjoint extension 2.2.3 Existence of the (differentiated) heat-kernel expansion 2.2.4 The heat-kernel coefficients 2.3 Local and Global Spectral Zeta Functions on Compact Manifolds 2.3.1 Weyl's asymptotic formulae 2.3.2 Spectral zeta functions 2.4 Effective Action, Effective Lagrangian and Green Functions 2.4.1 Comparison with the point-splitting regularization procedure 2.4.2 Green functions and zeta functions 2.4.3 Differential calculus of the heat kernel and local zeta functions 2.5 Noncompact Manifolds and Manifolds with a Boundary 2.6 The Stress-Energy Tensor and Field-Fluctuation Regularization 2.6.1 The stress-energy tensor 2.6.2 Zeta-function regularization of the stress-energy tensor and the field fluctuation 2.6.3 The regularized stress tensor and its properties 2.6.4 On the physical interpretation : Chapter 3 Generalized Spectra and Spectral Functions on Non-commutative Spaces 3.1 Extended Chowla-Selberg Formulae and Arbitrary Spectral Forms 3.2 Barnes and Related Zeta Functions 3.2.1 The two-dimensional case 3.2.2 The D-dimensional case 3.3 Spectral Zeta Functions for Scalar and Vector Fields on a Space-time with a Non-commutative Toroidal Part 3.3.1 Poles of the zeta function 3.3.2 Explicit analytic continuation of sa(s) 3.4 Applications to Quantum Field Theory in Non-commutative Space 3.4.1 Finite-temperature partition function 3.4.2 The spectral zeta function and the regularized vacuum energy 3.4.3 The regularized vacuum energy 3.4.4 High-temperature expansion Chapter 4 Spectral Functions of Laplace Operator on Locally Symmetric Spaces 4.1 Locally Symmetric Spaces of Rank One …… Chapter 5 Spinor Fields Chapter 6 Field Fluctuations and Related Variances Chapter 7 The Multiplicative Anomaly Chapter 8 Applications of the Multiplicative Anomaly Chapter 9 The Casimir Effect Appendix A Useful Mathematical Relations Appendix B The Wodzicki Residue Definitions and Conventions Bibliography Index |
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