Loop Variables in Topological Gravity

Abstract

We examine the relationship between covariant and canonical (Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1) and SO(3,1). The latter model can be considered as the simplest topological gravity theory in 3+1 dimensions. We carry out the canonical quantization of this model in both the connection and loop representations, for the two spatial topologies $T^3$ and $S^2\times S^1$.

20 pages, Latex

References in corpus (4)

• Representations of the holonomy algebras of gravity and non-Abelian gauge theories
• Recent Developments in Non-Perturbative Quantum Gravity
• Topological 2-form Gravity in Four Dimensions
• Wave Function of the Universe in Topological and in Einstein 2-form Gravity

Cited by in corpus (3)

• Topological Higher Gauge Theory - from BF to BFCG theory
• Gravity and BF theory defined in bounded regions
• Solvable model for quantum gravity