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arXiv · hep-th/9212144

Diff(SIGMA) and Metrics from Hamiltonian-TQFT's in 2+1 Dimensions

Roger Brooks
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Abstract

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 $M=Σ\times\IR$, 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.

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Roger Brooks. 1992-12-23. Diff(SIGMA) and Metrics from Hamiltonian-TQFT's in 2+1 Dimensions. https://doi.org/10.1142/s0217732393003585

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