Quantisation of 2+1 gravity for genus 2

Details Quantisation of 2+1 gravity for genus 2 Quantisation of 2+1 gravity for genus 2

1993-11-17

arxiv.org/abs/gr-qc/9311029v1

Phys.Rev. D50 (1994) 5125-5129

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.50.5125

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 $\th$ depends on the cosmological and Planck's constants.

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