Constants of the Motion and the Quantum Modular Group in (2+1) - Dimensional Gravity

Details Constants of the Motion and the Quantum Modular Group in (2+1) - Dimensional Gravity Constants of the Motion and the Quantum Modular Group in (2+1) - Dimensional Gravity

1997-10-30

arxiv.org/abs/gr-qc/9710131v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages Latex, uses mprocl.sty. Talk given in the Canonical Quantum Gravity session at the Eighth Marcel Grossmann meeting. Je

Scientific paper

Constants of motion are calculated for 2+1 dimensional gravity with topology R \times T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters, and the modular group is generated by these conserved quantities. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to the conformal algebra so(2,3).

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