Loop Variables in Topological Gravity

Details Loop Variables in Topological Gravity Loop Variables in Topological Gravity

1993-07-22

arxiv.org/abs/gr-qc/9307031v1

Class.Quant.Grav.11:883-896,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, Latex

Scientific paper

10.1088/0264-9381/11/4/008

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 $S^2\times S^1$.

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