A classical history theory: Geometrodynamics and general field dynamics regained

Details A classical history theory: Geometrodynamics and general field dynamics regained A classical history theory: Geometrodynamics and general field dynamics regained

1998-01-08

arxiv.org/abs/gr-qc/9801019v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, no figures, LaTeX

Scientific paper

Assuming that the Hamiltonian of a canonical field theory can be written in the form N H + N^i H_i, and using as the only input the actual choice of the canonical variables, we derive: (i) The algebra satisfied by H and H_i, (ii) any constraints, and (iii) the most general canonical representation for H and H_i. This completes previous work by Hojman, Kuchar and Teitelboim who had to impose a set of additional postulates, among which were the form of the canonical algebra and the requirement of path-independence of the dynamical evolution. A prominent feature of the present approach is the replacement of the equal-time Poisson bracket with one evaluated at general times. The resulting formalism is therefore an example of a classical history theory -- an interesting fact, especially in view of recent work by Isham et al.

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