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

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'.

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

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Cited by in corpus (14)

• Introduction to Loop Quantum Cosmology
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Anomaly-free cosmological perturbations in effective canonical quantum gravity
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Canonical Gravity with Fermions
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Quantization of Midisuperspace Models
• Fermions in Loop Quantum Cosmology and the Role of Parity
• Loop quantization of the Gowdy model with local rotational symmetry
• Towards Loop Quantization of Plane Gravitational Waves
• Minisuperspace models of discrete systems
• On plane gravitational waves in real connection variables
• Emergent modified gravity: Polarized Gowdy model on a torus