2+1 LATTICE GRAVITY

This is a theory of 2+1 gravity with a spacelike lattice and continuous time. It is derived from the Chern-Simons formulation of 2+1 gravity, in which the frame vectors are canonically conjugate to the SO(2, 1) connection. Dirac brackets are computed for the corresponding lattice variables: the link 3-vectors and the SO(2, 1) matrices which define parallel transport across the boundary between neighbouring faces. There is a set of first-class constraints, which state that the lattice analogues of torsion and curvature vanish locally. These generate local Lorentz rotations and independent translations of each lattice site. One finds the same complete set of observables as in the Chern-Simons formulation.