Invariants of 2+1 Quantum Gravity

Abstract

In [1,2] we established and discussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genus $g$ with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to $6g-6(g>1)$ is treated in detail with a precise classification for $g=1$ and $g=2$.

10 pages, plain TEX, no figures, DFTT 46/92

Cited by in corpus (19)

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• Equivalent Quantisations of (2+1)-Dimensional Gravity
• Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
• Cosmological measurements, time and observables in (2+1)-dimensional gravity
• The Quantum Modular Group in (2+1)-Dimensional Gravity
• Quantisation of 2+1 gravity for genus 2
• Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus
• QUANTUM ASPECTS OF 2+1 GRAVITY
• Center of the universal Askey--Wilson algebra at roots of unity
• Grafting and Poisson structure in (2+1)-gravity with vanishing cosmological constant
• Orbifold Riemann surfaces and geodesic algebras
• Independent Loop Invariants for 2+1 Gravity
• Representations of the q-deformed algebra U'_q(so_4)
• Symmetric Tamm-Dancoff q-oscillator: representation, quasi-Fibonacci nature, accidental degeneracy and coherent states
• A Quantum Goldman Bracket for Loops on Surfaces
• $\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus
• Extension of geodesic algebras to continuous genus
• Finite-dimensional irreducible modules of the universal Askey-Wilson algebra