$\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus

Details $\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus $\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus

1995-04-03

arxiv.org/abs/gr-qc/9504001v2

Gen.Rel.Grav. 27 (1995) 1001-1010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages plain TEX, extra comments and references added

Scientific paper

10.1007/BF02113082

The abstract quantum algebra of observables for 2+1 gravity is analysed in the limit of small cosmological constant. The algebra splits into two sets with an explicit phase space representation;~one set consists of $6g-6$ {\it commuting} elements which form a basis for an algebraic manifold defined by the trace and rank identities;~the other set consists of $6g-6$ tangent vectors to this manifold. The action of the quantum mapping class group leaves the algebra and algebraic manifold invariant. The previously presented representation for $g=2$ is analysed in this limit and reduced to a very simple form. The symplectic form for $g=2$ is computed.

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