Loop Quantization of Polarized Gowdy Model on $T^3$: Kinematical States and Constraint Operators

TL;DR

This paper develops the kinematical framework and constraint operators for loop quantum gravity applied to the polarized Gowdy model on T^3, enabling a better understanding of quantum states and dynamics.

Contribution

It constructs the kinematical Hilbert space and quantizes key operators, including the Hamiltonian constraint, for the Gowdy model in loop quantum gravity.

Findings

Kinematical Hilbert space constructed with well-defined holonomies and fluxes.

Volume operator and Gauss constraint quantized straightforwardly.

Discussion on effective operator approach for spatial correlations.

Abstract

In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is straightforward. Imposition of the Gauss constraint can be done on the kinematical Hilbert space to select subspace of gauge invariant states. We carry out the quantization of the Hamiltonian constraint making specific choices. Alternative choices are briefly discussed. It appears that to get spatial correlations reflected in the Hamiltonian constraint, one may have to adopt the so called `effective operator viewpoint'.