On canonical transformations between equivalent hamiltonian formulations of general relativity

A.M. Frolov1, N. Kiriushcheva2 and S.V. Kuzmin3

Abstract

Two Hamiltonian formulations of general relativity, due to Pirani, Schild and Skinner and Dirac, are considered. Both formulations, despite having different expressions for the constraints, allow one to derive four-dimensional diffeomorphism invariance. The relation between these two formulations at all stages of the Dirac approach to constrained Hamiltonian systems is analyzed. It is shown that the complete sets of their phase-space variables are related by a transformation which satisfies the ordinary condition of canonicity known for unconstrained Hamiltonians and, in addition, converts one total Hamiltonian into another, thus preserving form-invariance of generalized Hamiltonian equations for the constrained systems.

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