Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields

TL;DR

This paper provides a detailed Hamiltonian analysis of Gowdy models with massless scalar fields, focusing on topological differences and their implications for quantization and singularities.

Contribution

It offers a novel Hamiltonian formulation for coupled Gowdy models, highlighting topological effects and regularity constraints relevant for quantization.

Findings

Identified Hamiltonian structure for Gowdy models with scalar fields.

Analyzed topological effects on the Hamiltonian formulation.

Provided insights into the origin of singularities within the Hamiltonian framework.

Abstract

The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling of matter and those features that arise for the three-handle and three-sphere topologies that are not present in the well studied three torus case -in particular the polar constraints that come from the regularity conditions on the metric. As a byproduct of our analysis we will get an alternative understanding, within the Hamiltonian framework, of the appearance of initial and final singularities for these models.