Degeneracy and Para-supersymmetry of Dirac Hamiltonian in (2+1)- Spacetime

TL;DR

This paper explores the spectral properties and symmetries of a Dirac Hamiltonian for a spin 1/2 particle in (2+1)-dimensional curved spacetime with a magnetic monopole, revealing degeneracy groups, para-supersymmetry, and effects of angular deficits.

Contribution

It demonstrates the presence of SL(2,c) degeneracy, para-supersymmetry, and shape invariance in the Hamiltonian, and derives Dirac's quantization condition from representation theory.

Findings

Hamiltonians exhibit SL(2,c) degeneracy group

Existence of para-supersymmetry of arbitrary order

Angular deficit suppresses degeneracy and shape invariance

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.