Schrödinger quantization of linearly polarized Gowdy S1 × S2 and S3 models coupled to massless scalar fields

Abstract

In this paper, we will construct the Schr¨odinger representation for the linearly polarized Gowdy S1×S2 and S3 models coupled to massless scalar fields. Here the quantum states belong to a L2-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.