2008/09/07 by Alexei M. Frolov, A. M. Frolov, Frolov, A. M. +4
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.0809.1198
Conclusion is considerably extended, references are added, 20 pages
openalex publication_date 2008/09/07 · arxiv created 2011/07/14 · arxiv updated 2011/07/15 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.