1.

Record Nr.

UNINA9910458433803321

Autore

Simeone Claudio

Titolo

Deparametrization and path integral quantization of cosmological models [[electronic resource] /] / Claudio Simeone

Pubbl/distr/stampa

Singapore ; ; River Edge, NJ, : World Scientific, c2001

ISBN

981-277-837-3

Descrizione fisica

1 online resource (152 p.)

Collana

World scientific lecture notes in physics ; ; v. 69

Disciplina

523.1

Soggetti

Quantum gravity

Space and time

Path integrals

Gauge invariance

Hamiltonian systems

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Contents               ; 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: intrinsic 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 A toy model                        ; 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 cosmologies

5.1 String theory on background fields

Sommario/riassunto

The problem of time is a central feature of quantum cosmology: differing from ordinary quantum mechanics, in cosmology there is nothing "outside" the system which plays the role of clock, and this makes difficult the obtention of a consistent quantization. A possible solution is to assume that a subset of the variables describing the state of the universe can be a clock for the remaining of the system. Following this line, in this book a new proposal consisting in the previous identification of time by means of gauge fixation is applied to the quantization of homogeneous cosmological models.