宇宙模型中的非参数化及路径积分量子化/DEPARAMETRIZATION AND PATH INTEGRAL

In this book, homogeneous cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauges imposed on the gauge system are used to define a global phase time in terms of the canonical variables of the minisuperspaces. The procedure clearly shows how the geometry of the constraint surface restricts the choice of time. The consequences that this has for path integral quantization are discussed, and the transition amplitude is obtained for relativistic isotropic models, relativistic anisotropic models (Kantowski-Sachs and Taub) and isotropic string cosmologies. A complete chapter about the application of the deparametrization program to the usual canonical quantization scheme is also included.

Preface
Chapter 1 Introduction
Chapter 2 The gravitational field as a constrained Hamiltonian system
2.1 Momentum and Hamiltonian constraints
2.2 Minisuperspaces as constrained systems
2.3 Quantization
2.3.1 Canonical quantization
2.3.2 Path integral quantization
Chapter 3 Deparametrization and path integral quantization
3.1 The identification of time
3.1.1 Gauge fixation and deparametrization
3.1.2 Topology of the constraint surface: intrmsic and extrinsic time
3.2 Gauge-invariant action for a parametrized system
3.2.1 End point terms
3.2.2 Observables and time
3.2.3 Non separable constraints
3.3 Path integral
3.3.1 General formalism
3.3.2 The function f and the reduced Hamiltonian. Unitarity
3.4 Examples
3.4.1 Feynman propagator for the Klein-Gordon equation
3.4.2 The ideal clock
3.4.3 Transition probability for empty Friedmann-Robertson-Walker universes
Chapter 4 Homogeneous relativistic cosmologies
4.1 Isotropic universes
4.1.1 Atoymodel
4.1.2 True degrees of freedom
4.1.3 A more general constraint
4.1.4 Extrinsic time. The closed "de Sitter" universe
4.1.5 Comment
4.2 Anisotropic universes
4.2.1 The Kantowski-Sachs universe
4.2.2 The Taub universe
4.2.3 Other anisotropic models
Chapter 5 String eosmologies
5.1 String theory on background fields
5.2 String cosmological models
5.3 Path integral quantization
5.3.1 Gauge-invariant action
5.3.2 Extrinsic time
5.3.3 Intrinsic time and path integral
5.3.4 Summary
Chapter 6 Canonical quantization
6.1 Approximate solutions of the Wheeler-DeWitt equation
6.2 Gauge fixation and SchrSdinger equation for isotropic models
6.3 The Taub universe
6.3.1 Standard procedure
6.3.2 Boundary conditions and Schredinger equation
6.3.3 Wheeler-DeWitt equation with extrinsic time
6.4 String cosmologies
6.4.1 Wheeler-DeWitt equation
6.4.2 SchrSdinger equation
Chapter 7 Discussion
Appendix A Constrained Hamiltonian systems
Appendix B Path integral and inner product
Appendix C End point terms
Appendix D An extrinsic time for the Taub universe
Appendix E Free-particle constraint for minisuperspaces
Bibliography
Index