Viqar Husain and Oliver Winkler 2004 Class. Quantum Grav. 21 941 doi:10.1088/0264-9381/21/4/014
Viqar Husain1 and Oliver Winkler2
Show affiliationsWe 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.
04.60.Nc Lattice and discrete methods
83C27 Lattice gravity, Regge calculus and other discrete methods
Issue 4 (21 February 2004)
Received 17 September 2003
Published 14 January 2004
Viqar Husain and Oliver Winkler 2004 Class. Quantum Grav. 21 941
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