Discrete Hamiltonian evolution and quantum gravity

Details Discrete Hamiltonian evolution and quantum gravity Discrete Hamiltonian evolution and quantum gravity

2003-08-05

arxiv.org/abs/gr-qc/0308011v2

Class.Quant.Grav. 21 (2004) 941-950

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, minor changes, to appear in CQG

Scientific paper

10.1088/0264-9381/21/4/014

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization.

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