Deparametrization and Path Integral Quantization of Cosmological ModelsThe 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. Both path integral and canonical formulations are studied for relativistic and string cosmologies; in particular, a complete chapter about low energy string cosmology is included. The required basic concepts (as for example the Hamiltonian formulation of General Relativity) are reviewed, so that the book can be of interest not only for a researcher but also for a student. |
Contents
Introduction | 1 |
The gravitational field as a constrained | 7 |
2 | 13 |
Homogeneous relativistic cosmologies | 45 |
String cosmologies | 77 |
Canonical quantization | 91 |
Appendix A Constrained Hamiltonian systems | 111 |
An extrinsic time for the Taub universe | 129 |
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Deparametrization and Path Integral Quantization of Cosmological Models Claudio Simeone Limited preview - 2002 |
Common terms and phrases
Barvinsky boundaries canonical quantization canonical transformation canonical variables classical constraint surface coordinate Q coordinates and momenta corresponding cosmological constant cosmological models define definite sign degrees of freedom deparametrization dilaton dynamical end point terms equivalent evolution extrinsic formalism gauge choice gauge fixation gauge transformation gauge-invariant action given global phase gravitational Gribov Hájícek Hamilton-Jacobi equation Hamiltonian constraint Hamiltonian form Hence homogeneous hypersurface ideal clock inner product intrinsic invariant isotropic Kantowski-Sachs Kuchař linear metric minisuperspace momentum monotonic function obtain original coordinates original variables P₁ parametrized system path integral quantization phase space Phys physical degree Poisson bracket positive definite possible potential problem procedure propagator quantum reduced Hamiltonian reduced system relativistic result Schrödinger equation sheet solutions spacetime string cosmologies string theory T₁ Taub universe tion transition amplitude true degrees true Hamiltonian vanish wave function Wheeler-DeWitt equation π² Πρ ΠΩ მი