Evolution Operators for Linearly Polarized Two-Killing Cosmological Models

TL;DR

This paper develops a method to derive exact evolution operators for a class of quantum cosmological models with two symmetries, analyzing their unitarity and Fock space representations.

Contribution

It provides a general, non-perturbative approach to construct and analyze evolution operators in linearly polarized two-Killing cosmological models.

Findings

Derived closed-form evolution operators for the models.

Identified conditions for unitary evolution.

Analyzed Fock space representations of the operators.

Abstract

We give a general procedure to obtain non perturbative evolution operators in closed form for quantized linearly polarized two Killing vector reductions of general relativity with a cosmological interpretation. We study the representation of these operators in Fock spaces and discuss in detail the conditions leading to unitary evolutions.