Gravity in Physics, Quantum Physics, Physics of Time, Calculus

Deparametrization and Path Integral Quantization of Cosmological Models (World Scientific Lecture Notes in Physics)

Name: Deparametrization and Path Integral Quantization of Cosmological Models (World Scientific Lecture Notes in Physics)
Author: Claudio Simeone
ISBN: 9789810247416

by Claudio Simeone

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Overview

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.

Synopsis

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. 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.