Degeneracy and Para-supersymmetry of Dirac Hamiltonian in (2+1)- Spacetime
arXiv:hep-th/9904166 · doi:10.1063/1.532965
Abstract
The quantum mechanics of a spin 1/2 particle on a locally spatial constant curvature part of a (2+1)- spacetime in the presence of a constant magnetic field of a magnetic monopole has been investigated. It has been shown that these 2-dimensional Hamiltonians have the degeneracy group of SL(2,c), and para-supersymmetry of arbitrary order or shape invariance. Using this symmetry we have obtained its spectrum algebraically. The Dirac's quantization condition has been obtained from the representation theory. Also, it is shown that the presence of angular deficit suppresses both the degeneracy and shape invariance.
31 pages, Latex, no figures, to be published in J. Math. Phys