Classical and quantum aspects of degenerate metric fields

Summary

Abstract

Degenerate space-time metrics are discussed in the framework of gravitation in interaction with scalar fields. Minisuperspace quantisations are effected leading to coherent states that exhibit enhanced fluctuations in the vicinity of classical cosmological loci. An alternative approach for implementing the Hamiltonian constraint is offered in terms of a spinor state space and an analysis of solutions to the scalar field equation on a 2-dimensional topologically non-trivial manifold with a degenerate metric is summarised.

Introduction

In the absence of a viable quantum description of the gravitational field attention is sometimes directed to the so called “mini-superspace” models [1] in which all but a small number of degrees of freedom of the gravitational field are suppressed and the dynamics is reduced from field theory to quantum mechanics. Such a programme is fraught with both conceptual and technical difficulties. It ignores many effects that may be of relevance in determining a viable quantum description. One restricts to quantum states describing highly symmetric geometries that possess a preferred class of spacelike foliations that may be used to order temporal phenomena in a classical spacetime. Even within this restricted framework there is no preferred way to effect a quantisation of Einstein's equations of motion tensorial nature of these equations gives rise to a constrained canonical system and there is no known criterion that singles out a particular mapping from the classical constraints to a set of quantum operators on a Hilbert space.