Mode decomposition and unitarity in quantum cosmology, Talk given at the Second Meeting on Constrained Dynamics and Quantum gravity, Santa Margherita Ligure, September 17-21, 1996

TL;DR

This paper explores a novel approach to defining positive and negative frequencies in quantum cosmology without relying on symmetries, revealing an underlying unitarity structure and connecting to algebraic quantization methods.

Contribution

It proposes a new strategy for generalizing frequency notions in minisuperspace quantum cosmology with positive potentials, highlighting a unitarity structure and potential links to refined algebraic quantization.

Findings

A new method for frequency generalization in non-symmetric models

Identification of an underlying unitarity structure in quantum cosmology

Potential connection to refined algebraic quantization schemes

Abstract

Contrary to common belief, there are perspectives for generalizing the notion of positive and negative frequency in minisuperspace quantum cosmology, even when the wave equation does not admit symmetries. We outline a strategy in doing so when the potential is positive. Also, an underlying unitarity structure shows up. Starting in the framework of the Klein-Gordon type quantization, I am led to a result that relies on global features on the model, and that is possibly related to structures encountered in the refined algebraic quantization scheme.