Constants of motion and the conformal anti - de Sitter algebra in (2+1)-Dimensional Gravity

Details Constants of motion and the conformal anti - de Sitter algebra in (2+1)-Dimensional Gravity Constants of motion and the conformal anti - de Sitter algebra in (2+1)-Dimensional Gravity

1997-07-15

arxiv.org/abs/gr-qc/9707032v1

Int.J.Mod.Phys.D6:545-562,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, Plain Tex, No Figures

Scientific paper

10.1142/S0218271897000339

Constants of motion are calculated for 2+1 dimensional gravity with topology R x 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. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to that of the conformal algebra so(2,3). The modular group appears as a discrete subgroup of the conformal group. Its quantum action is generated by these conserved quantities.

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