The simplest Regge calculus model in the canonical form

Details The simplest Regge calculus model in the canonical form The simplest Regge calculus model in the canonical form

1999-12-28

arxiv.org/abs/gr-qc/9912112v1

Phys.Lett. B477 (2000) 248-252

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 7 pages

Scientific paper

10.1016/S0370-2693(00)00201-X

Dynamics of a Regge three-dimensional (3D) manifold in a continuous time is considered. The manifold is closed consisting of the two tetrahedrons with identified corresponding vertices. The action of the model is that obtained via limiting procedure from the general relativity (GR) action for the completely discrete 4D Regge calculus. It closely resembles the continuous general relativity action in the Hilbert-Palatini (HP) form but possesses finite number of the degrees of freedom. The canonical structure of the theory is described. Central point is appearance of the new relations with time derivatives not following from the Lagrangian but serving to ensure completely discrete 4D Regge calculus origin of the system. In particular, taking these into account turns out to be necessary to obtain the true number of the degrees of freedom being the number of linklengths of the 3D Regge manifold at a given moment of time.

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