Loop Quantization of Polarized Gowdy Model on $T^3$: Classical Theory

Abstract

The vacuum Gowdy models provide much studied, non-trivial midi-superspace examples. Various technical issues within Loop Quantum Gravity can be studied in these models as well as one can hope to understand singularities and their resolution in the loop quantization. The first step in this program is to reformulate the model in real connection variables in a manner that is amenable to loop quantization. We begin with the unpolarized model and carry out a consistent reduction to the polarized case. Carrying out complete gauge fixing, the known solutions are recovered.

20 pages, no figures. Final version; to appear in Classical and Quantum Gravity. Additional References included

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Cited by in corpus (15)

• Introduction to Loop Quantum Cosmology
• Anomaly-free cosmological perturbations in effective canonical quantum gravity
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Quantization of Midisuperspace Models
• Covariance in models of loop quantum gravity: Gowdy systems
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Dynamics and entanglement in spherically symmetric quantum gravity
• Loop quantization of the Gowdy model with local rotational symmetry
• Loop Quantization of Polarized Gowdy Model on $T^3$: Kinematical States and Constraint Operators
• Towards Loop Quantization of Plane Gravitational Waves
• On plane gravitational waves in real connection variables
• Emergent modified gravity: Polarized Gowdy model on a torus
• Lessons for loop quantum gravity from emergent modified gravity
• Classical Polymerization of the Bianchi I Model with Deformed Poisson Structure