Regge calculus in the canonical form

Details Regge calculus in the canonical form Regge calculus in the canonical form

1993-10-03

arxiv.org/abs/gr-qc/9310004v1

Gen.Rel.Grav. 27 (1995) 583-603

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages,Plain LaTeX,BINP 93-42

Scientific paper

(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used supplemented with appropriate bilinear constraints. In these variables the action can be made quasipolinomial with $\arcsin$ as the only deviation from polinomiality. In comparison with analogous formalism in the continuum theory classification of constraints changes: some of them disappear, the part of I class constraints including Hamiltonian one become II class (and vice versa, some new constraints arise and some II class constraints become I class). As a result, the number of the degrees of freedom coincides with the number of links in 3-dimensional leaf of foliation. Moreover, in empty space classical dynamics is trivial: the scale of timelike links become zero and spacelike links are constant.

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