On canonical transformations between equivalent Hamiltonian formulations of General Relativity

Details On canonical transformations between equivalent Hamiltonian formulations of General Relativity On canonical transformations between equivalent Hamiltonian formulations of General Relativity

2008-09-07

arxiv.org/abs/0809.1198v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Conclusion is considerably extended, references are added, 20 pages

Scientific paper

Two Hamiltonian formulations of General Relativity, due to Pirani, Schild and Skinner (Phys. Rev. 87, 452, 1952) and Dirac (Proc. Roy. Soc. A 246, 333, 1958), are considered. Both formulations, despite having different expressions for constraints, allow one to derive four-dimensional diffeomorphism invariance. The relation between these two formulations at all stages of the Dirac approach to the 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 constrained systems.

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