The Quantum Configuration Space of Loop Quantum Cosmology

Abstract

The article gives an account of several aspects of the space known as the Bohr compactification of the line, featuring as the quantum configuration space in loop quantum cosmology, as well as of the corresponding configuration space realization of the so-called polymer representation. Analogies with loop quantum gravity are explored, providing an introduction to (part of) the mathematical structure of loop quantum gravity, in a technically simpler context.

14 pages. Minor changes, typos corrected, 1 reference added. To appear in Class. Quantum Grav

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• Photons from quantized electric flux representations
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Cited by in corpus (44)

• Introduction to Loop Quantum Cosmology
• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
• Background independent quantization and the uncertainty principle
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Hybrid quantization of an inflationary model: The flat case
• Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations
• On effective loop quantum geometry of Schwarzschild interior
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Hybrid Loop Quantum Cosmology: An Overview
• Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields with a time dependent mass in ultrastatic spacetimes
• Quantum gravity and the Coulomb potential
• Propagators in Polymer Quantum Mechanics
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Polymer Bose--Einstein Condensates
• Group theoretical Quantization of Isotropic Loop Cosmology
• Loop Quantum Cosmology: A cosmological theory with a view
• Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime
• Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime
• New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes
• Statistical Thermodynamics of Polymer Quantum Systems
• Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology
• Tunneling in Polymer Quantization and the Quantum Zeno Effect
• The Koslowski-Sahlmann representation: Quantum Configuration Space
• A Brief Overview of Results about Uniqueness of the Quantization in Cosmology
• Polymer-Fourier quantization of the scalar field revisited
• The symplectic group in Polymer Quantum Mechanics
• Quasi-probability distributions in Loop Quantum Cosmology
• Topics of Measure Theory on Infinite Dimensional Spaces
• Bounds on the Polymer Scale from Gamma Ray Bursts
• What do gravitational wave detectors say about polymer quantum effects?
• On the space of generalized fluxes for loop quantum gravity
• Instanton solutions on the polymer harmonic oscillator
• Entropy and entanglement in polymer quantization
• Projective Structures in Loop Quantum Cosmology
• Frustration of resonant preheating by exotic kinetic terms
• Taming Fluctuations for Gaussian States in Loop Quantum Cosmology
• The relation between the symplectic group $Sp(4,\mathbb{R})$ and its Lie algebra: its application in polymer quantum mechanics
• An open scattering model in polymerized quantum mechanics
• Local Properties of Measures in Quantum Field Theory and Cosmology
• Superfluids in Polymer Quantum Mechanics
• Polymer quantization in the Bogoliubov's regime for a homogeneous one-dimensional Bose-Einstein condensate
• Polymer quantum mechanics on compact configuration spaces
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model
• Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes