Quantization of Midisuperspace Models

Abstract

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.

To appear in Living Review in Relativity

References in corpus (35)

• Loop Quantum Dynamics of the Schwarzschild Interior
• Black holes in loop quantum gravity: the complete space-time
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• The Superspace of Geometrodynamics
• Loop quantization of spherically symmetric midi-superspaces
• Self-dual Black Holes in LQG: Theory and Phenomenology
• Black hole interior from loop quantum gravity
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Quantum Gowdy $T^3$ model: A uniqueness result
• Quantum Gowdy $T^3$ model: A unitary description
• Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
• Complete, Single-Horizon Quantum Corrected Black Hole Spacetime
• Hawking radiation from the quantum Lemaitre-Tolman-Bondi model
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• The Volume Operator in Spherically Symmetric Quantum Geometry
• Gravitational collapse in loop quantum gravity
• Dirac-like approach for consistent discretizations of classical constrained theories
• Uniqueness of the Fock representation of the Gowdy $S^1\times S^2$ and $S^3$ models
• Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields
• Consistent and mimetic discretizations in general relativity
• Loop Quantization of Polarized Gowdy Model on $T^3$: Kinematical States and Constraint Operators
• Loop Quantization of Polarized Gowdy Model on $T^3$: Classical Theory
• Evolution Operators for Linearly Polarized Two-Killing Cosmological Models
• Loop quantum gravity and black hole singularity
• Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields
• Spectrum and Statistical Entropy of AdS Black Holes
• Schrodinger representation for the polarized Gowdy model
• Probing Quantized Einstein-Rosen Waves with Massless Scalar Matter
• Schrodinger quantization of linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields
• Quantum Einstein-Rosen waves: Coherent states and n-point functions
• Signatures of an Emergent Gravity from Black Hole Entropy

Cited by in corpus (22)

• Introduction to Loop Quantum Cosmology
• Where does the physics of extreme gravitational collapse reside?
• The Smallest Shape Spaces. I. Shape Theory Posed, with Example of 3 Points on the Line
• Creation of the universe with a stealth scalar field
• Covariant phase space for gravity with boundaries: metric vs tetrad formulations
• Unitary evolution of the quantum universe with a Brown-Kuchar dust
• Big Bang Singularity Resolution In Quantum Cosmology
• Hamiltonian description of the parametrized scalar field in bounded spatial regions
• Dark Horse, Dark Matter: Revisiting the SO(16)x SO(16)' Nonsupersymmetric Model in the LHC and Dark Energy Era
• Schwarzschild Mass Uncertainty
• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
• 3D gravity with dust: classical and quantum theory
• Orthogonal gauge fixing of first order gravity
• Hamiltonian dynamics of the parametrized electromagnetic field
• Maxwell-like picture of General Relativity and its Planck limit
• Testing the problem of time with cold atoms
• Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions
• Exact time-dependent states for throat quantized toroidal AdS black holes
• Quantum Computing for Inflationary, Dark Energy and Dark Matter Cosmology
• Strings, Topological Change and Dark Matter
• Does quantum gravity relate the constants of nature?
• Bianchi cosmologies in a Thurston-based theory of gravity