) and Metrics from Hamiltonian–TQFT’s in 2+1 Dimensions

The constraints of BF topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of Topological Quantum Field Theories (TQFT’s). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for 2+1 and 1+1 dimensional space-times foliated as M = Σ× IR, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained. CTP #2175 December 1992 hep-th/yymmnn ⋆ This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069.