Polymer quantization of CGHS model- I
arXiv:gr-qc/0606069 · doi:10.1088/0264-9381/24/20/005
Abstract
We present a polymer(loop) quantization of a two dimensional theory of dilatonic gravity known as the CGHS model. We recast the theory as a parametrized free field theory on a flat 2-dimensional spacetime and quantize the resulting phase space using techniques of loop quantization. The resulting (kinematical) Hilbert space admits a unitary representation of the spacetime diffeomorphism group. We obtain the complete spectrum of the theory using a technique known as group averaging and perform quantization of Dirac observables on the resulting Hilbert space. We argue that the algebra of Dirac observables gets deformed in the quantum theory. Combining the ideas from parametrized field theory with certain relational observables, evolution is defined in the quantum theory in the Heisenberg picture. Finally the dilaton field is quantized on the physical Hilbert space which carries information about quantum geometry.
50 pages, 2 figures
References in corpus (28)
- Evanescent Black Holes
- Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
- Geometrodynamics of Schwarzschild Black Holes
- Partial and Complete Observables for Hamiltonian Constrained Systems
- Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
- Lectures on 2D gravity and 2D string theory (TASI 1992)
- Black Hole Evaporation in 1+1 Dimensions
- Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
- Quantum Emission from Two-Dimensional Black Holes
- On the Generality of Refined Algebraic Quantization
- Polymer and Fock representations for a Scalar field
- Physical States in Matter-Coupled Dilaton Gravity
- Relation between polymer and Fock excitations
- Fadeev-Popov Ghosts and 1+1 Dimensional Black Hole Evaporation
- Quantum Theories of Dilaton Gravity
- Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
- Functional Schroedinger and BRST Quantization of (1+1)--Dimensional Gravity
- On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
- The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
- Covariant gauge fixing and Kuchar decomposition
- Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes
- Time evolution of observable properties of parametrized systems
- Unitary Theory of Evaporating 2D Black Holes
- Time evolution and observables in constrained systems
- Quantum gravity effects in the CGHS model of collapse to a black hole
- Perennials and the Group-Theoretical Quantization of a Parametrized Scalar Field on a Curved Background
- Polymer quantization of CGHS model- I
- DDF and Pohlmeyer invariants of (super)string
Cited by in corpus (7)
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- Loop Quantum Gravity and Cosmology: A dynamical introduction
- Quantum geometry with a nondegenerate vacuum: a toy model
- Quantum Space-times: Beyond the Continuum of Minkowski and Einstein
- Asymptotic Flatness and Quantum Geometry
- Quantum gravity effects on space-time