Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations

Details Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations

1997-07-16

arxiv.org/abs/gr-qc/9707039v3

J.Math.Phys. 39 (1998) 3805-3816

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages; requires amsart, amssymb, amsmath; cleaned up slightly. To appear in J. Math. Phys

Scientific paper

10.1063/1.532469

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.

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