Schrodinger quantization of linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields

TL;DR

This paper develops a Schrödinger representation for specific Gowdy models with scalar fields, completing their quantization and enabling new analysis of their quantum states in a Gaussian measure framework.

Contribution

It introduces a Schrödinger quantization for Gowdy $S^1\times S^2$ and $S^3$ models, extending previous Fock scheme results and providing a new framework for physical investigations.

Findings

Constructed the Schrödinger representation for the models.

Analyzed the support of the Gaussian measure in the quantum configuration space.

Completed the quantization of these models in a new framework.

Abstract

In this paper we will construct the Schrodinger representation for the linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields. Here the quantum states belong to a $L^2$-space for a suitable quantum configuration space endowed with a Gaussian measure, whose support is analyzed. This study completes the quantization of these systems previously performed in the Fock scheme, and provides a specially useful framework to address physically relevant questions.