A Spinor Model for Quantum Cosmology

TL;DR

This paper introduces a spinor wave equation approach to quantum cosmology, providing a new interpretation of Wheeler-DeWitt solutions and a method to connect quantum states with classical cosmological geometries.

Contribution

It presents a novel spinor model for quantum cosmology that incorporates a relative probability interpretation and a parametrization of classical solutions in minisuperspace.

Findings

The model accommodates signature change in classical metrics.

A prescription for classical time in quantum cosmology is proposed.

Application demonstrated in a 2D dilaton gravity model.

Abstract

The question of the interpretation of Wheeler-DeWitt solutions in the context of cosmological models is addressed by implementing the Hamiltonian constraint as a spinor wave equation in minisuperspace. We offer a relative probability interpretation based on a non-closed vector current in this space and a prescription for a parametrisation of classical solutions in terms of classical time. Such a prescription can accommodate classically degenerate metrics describing manifolds with signature change. The relative probability density, defined in terms of a Killing vector of the Dewitt metric on minisuperspace, should permit one to identify classical loci corresponding to geometries for a classical manifold. This interpretation is illustrated in the context of a quantum cosmology model for two-dimensional dilaton gravity.