Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations

The constraint algebra derived in Class. Quantum Grav. 14 (1997), 1851--1864 is generated explicitly from a formulation of general relativity in which both the metric and vielbein are independent degrees of freedom. The standard form of the Hamiltonian is composed of the Hamiltonian and momentum con...

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Autor principal: Clayton, M.A.
Lenguaje:eng
Publicado: 1997
Materias:
General Relativity and Cosmology
Acceso en línea:https://dx.doi.org/10.1063/1.532469
http://cds.cern.ch/record/330199
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author Clayton, M.A.
author_facet Clayton, M.A.
author_sort Clayton, M.A.
collection CERN
description The constraint algebra derived in Class. Quantum Grav. 14 (1997), 1851--1864 is generated explicitly from a formulation of general relativity in which both the metric and vielbein are independent degrees of freedom. The standard form of the Hamiltonian is composed of the Hamiltonian and momentum constraints, as well as constraints that generate spatial frame transformations; all appearing as primary, first class constraints on phase space. From these results, the conditions that must be satisfied by the generators of any diffeomorphism invariant, non-derivatively coupled, classical field are derived.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1997
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spelling cern-3301992023-03-14T17:57:36Zdoi:10.1063/1.532469http://cds.cern.ch/record/330199engClayton, M.A.Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame TransformationsGeneral Relativity and CosmologyThe constraint algebra derived in Class. Quantum Grav. 14 (1997), 1851--1864 is generated explicitly from a formulation of general relativity in which both the metric and vielbein are independent degrees of freedom. The standard form of the Hamiltonian is composed of the Hamiltonian and momentum constraints, as well as constraints that generate spatial frame transformations; all appearing as primary, first class constraints on phase space. From these results, the conditions that must be satisfied by the generators of any diffeomorphism invariant, non-derivatively coupled, classical field are derived.Einstein's general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as constraints that generate spatial frame transformations---all appearing as primary, first class constraints on phase space. The formalism encompasses the standard coordinate frame and vielbein approaches to general relativity, and the constraint algebra derived herein reproduces known results in either limit.gr-qc/9707039CERN-TH-97-168CERN-TH-97-168oai:cds.cern.ch:3301991997-07-17
spellingShingle General Relativity and Cosmology
Clayton, M.A.
Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations
title Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations
title_full Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations
title_fullStr Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations
title_full_unstemmed Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations
title_short Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations
title_sort canonical general relativity: the diffeomorphism constraints and spatial frame transformations
topic General Relativity and Cosmology
url https://dx.doi.org/10.1063/1.532469
http://cds.cern.ch/record/330199
work_keys_str_mv AT claytonma canonicalgeneralrelativitythediffeomorphismconstraintsandspatialframetransformations

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