| Description |
1 online resource |
| 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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
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. B |
| Notes |
Print version record |
| Subject |
Quantum gravity.
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Space and time.
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Path integrals.
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Gauge invariance.
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Hamiltonian systems.
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Gauge invariance
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Hamiltonian systems
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Path integrals
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Quantum gravity
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Space and time
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| Form |
Electronic book
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| ISBN |
1299742041 |
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9781299742048 |
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9789812778376 |
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9812778373 |
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