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

J. E. Nelson·T. Regge
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Abstract

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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J. E. Nelson, T. Regge. 1995-04-13. $\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus. https://doi.org/10.1007/bf02113082

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