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

Banerjee, Kinjal; Date, Ghanashyam

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

Authors

Description

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'.
26 pages, no figures. Version 2 accepted for publication. This has the sub-title changed, introduction modified for comments on references, small errors corrected and references updated