Quantisation of 2+1 gravity for genus 2

Abstract

In [1,2] we established and discussed the algebra of observables for $2+1$ gravity at both the classical and quantum level, and gave a systematic discussion of the reduction of the expected number of independent observables to $6g-6(g>1)$. In this paper the algebra of observables for the case $g=2$ is reduced to a very simple form. A Hilbert space of state vectors is defined and its representations are discussed using a deformation of the Euler-Gamma function. The deformation parameter $þ$ depends on the cosmological and Planck's constants.

11 pages, 2 figures available from authors, DFTT 54/93

References in corpus (2)

• Invariants of 2+1 Quantum Gravity
• Equivalent Quantisations of (2+1)-Dimensional Gravity

Cited by in corpus (11)

• Quantum Gravity as a Dissipative Deterministic System
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
• Comparative Quantizations of (2+1)-Dimensional Gravity
• Large Diffeomorphisms in (2+1)-Quantum Gravity on the Torus
• The Quantum Modular Group in (2+1)-Dimensional Gravity
• QUANTUM ASPECTS OF 2+1 GRAVITY
• Polygon model from first order gravity
• (2+1) gravity for higher genus in the polygon model
• A Quantum Goldman Bracket for Loops on Surfaces
• $\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus