Canonical Quantization of Cylindrical Gravitational Waves

Kuchař, Karel

doi:10.1103/physrevd.4.955

Cited by 211 publications

(308 citation statements)

References 21 publications

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“…In certain special cases the isometry group of the D-dimensional metric is such that it allows for a reduction to D 1 = 2. Important examples for D = 4 are toroidal reduction [273,189,178,225,56] and spherical reduction [36,412,33,409,205,324,407,244,276,295,195]. The latter is of special importance, because it covers the Schwarzschild BH.…”

Section: Spherically Reduced Gravitymentioning

confidence: 99%

“…The prehistory of canonical quantization of gravity involves the seminal papers of Arnowitt, Deser and Misner [7], Wheeler [435] and DeWitt [121] which led to Misner's "minisuperspace quantization" program [331], where almost all degrees of freedom were frozen by symmetry requirements. Kuchař extended these techniques to "midisuperspace quantization" for the explicit example of cylindrical gravitational waves [273], i.e. to a system with field degrees of freedom, albeit still using symmetry requirements in order to simplify the formalism.…”

Section: Canonical Quantizationmentioning

confidence: 99%

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Dilaton gravity in two dimensions

2002

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The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important examples of spherically symmetric Black Holes, together with string inspired models, belong to this class, valuable knowledge can also be gained for these systems in the quantum case. In the last decade new insights regarding the exact quantization of the geometric part of such theories have been obtained. They allow a systematic quantum field theoretical treatment, also in interactions with matter, without explicit introduction of a specific classical background geometry. The present review tries to assemble these results in a coherent manner, putting them at the same time into the perspective of the quite large literature on this subject.

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Section: Spherically Reduced Gravitymentioning

confidence: 99%

Section: Canonical Quantizationmentioning

confidence: 99%

Dilaton gravity in two dimensions

2002

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“…Since 'sufficiently many' evidently includes 'infinitely many', a minimal requirement on G(E) is that it be infinite dimensional. [7]), the left square bracket denotes the fact that for each value of A, f A is a functional of the embedding and the round bracket denotes the fact that f A is a function of x. Using our notation in the discussion above, we have…”

Section: Problems Withĥ G and Their Resolution In Terms Of A Treatmentioning

confidence: 99%

“…7 We expect that the vanishing of the constraints C A (x) is equivalent to the vanishing of the smeared constraints C(ξ) provided that the latter holds for sufficiently many ξ A (X). Since 'sufficiently many' evidently includes 'infinitely many', a minimal requirement on G(E) is that it be infinite dimensional.…”

Section: Problems Withĥ G and Their Resolution In Terms Of A Treatmentioning

confidence: 99%

“…They analyse the case of an axisymmetric scalar field evolving along arbitrary axisymmetric foliations of a flat 2+1 dimensional spacetime. This system is equivalent, via Kuchař's canonical transformation [7], to the midisuperspace of cylindrically symmetric (1 polarization) gravitational fields. Reference [6] obtains a non-unitary result for generic axisymmetric scalar field evolution by showing that the action of generic radial diffeomorphisms on the scalar field operators is not unitarily implementable (see [6] for details).…”

Section: Introductionmentioning

confidence: 99%

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Dirac quantization of parametrized field theory

Varadarajan

2007

Phys. Rev. D

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Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary (and in general, curved) foliations of the flat spacetime instead of only the usual flat foliations, by treating the 'embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schrodinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one. This formal Schrodinger picture-based quantization is unitarily equivalent to the standard Heisenberg picture based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization.We construct a Dirac quantization of PFT, unitarily equivalent to the standard Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are powerful enough to super-cede the no-go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints and group averaging techniques. The difference between the 1+1 dimensional case and the case of higher spacetime dimensions is that for the latter, only finite gauge transformations are defined in quantum theory not the infinitesimal ones.

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Problem of time in quantum gravity

2012

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The Problem of Time occurs because the 'time' of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the very early universe. Emphasis in this Review is on the Problem of Time being multi-faceted and on the nature of each of the eight principal facets. Namely, the Frozen Formalism Problem, Configurational Relationalism Problem (formerly Sandwich Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time, Problem of Beables (alias Problem of Observables) and Spacetime Reconstruction/Replacement Problem. Strategizing in this Review is not just centred about the Frozen Formalism Problem facet, but rather about each of the eight facets. Particular emphasis is placed upon A) relationalism as an underpinning of the facets and as a selector of particular strategies (especially a modification of Barbour relationalism, though also with some consideration of Rovelli relationalism). B) Classifying approaches by the full ordering in which they embrace constrain, quantize, find time/history and find observables, rather than only by partial orderings such as "Dirac-quantize". C) Foliation (in)dependence and Spacetime Reconstruction for a wide range of physical theories, strategizing centred about the Problem of Beables, the Patching Approach to the Global Problem of Time, and the role of the question-types considered in physics. D) The Halliwell-and Gambini-Porto-Pullin-type combined Strategies in the context of semiclassical quantum cosmology.

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Canonical Quantization of Cylindrical Gravitational Waves

Cited by 211 publications

References 21 publications

Dilaton gravity in two dimensions

Dilaton gravity in two dimensions

Dirac quantization of parametrized field theory

Problem of time in quantum gravity

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