2+1-Gravity and The Embedding its Dynamiycal Symmetry and Para-Supersymmetry into SO(4,c) Group

Details 2+1-Gravity and The Embedding its Dynamiycal Symmetry and Para-Supersymmetry into SO(4,c) Group 2+1-Gravity and The Embedding its Dynamiycal Symmetry and Para-Supersymmetry into SO(4,c) Group

1999-04-24

arxiv.org/abs/gr-qc/9904060v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 page, Latex, no figures

Scientific paper

Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its spatial part and a constant magnetic field of a magnetic monopole together with deficit of angle at the location of point mass. The quantum mechanics of a point particle in these spacetimes in the absence of angular deficit has been solved algebraically both relativistically and non-relativistically. It has been also shown that these 2-dimensional Hamiltonians have the degeneracy group of GL(2,c) type and para-supersymmetry of arbitrary order or shape invariance, which is originated from a SO(4,c) group.

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