ON DIFFEOMORPHISM INVARIANCE FOR LATTICE THEORIES

We consider the role of the diffeomorphism constraint in the quantizat ion of lattice formulations of diffeomorphism invariant theories of co nnections. It has been argued that in working with abstract lattices o ne automatically takes care of the diffeomorphism constraint in the qu antum theory. We use two systems in order to show that imposing the di ffeomorphism constraint is imperative to obtain a physically acceptabl e quantum theory. First, we consider 2 + 1 gravity where an exact latt ice formulation is available. Next, general theories of connections fo r compact gauge groups are treated, where the quantum theories are kno wn - for both the continuum and the lattice - and can be compared. (C) 1997 Elsevier Science B.V.