Dynamical supersymmetry of the magnetic monopole and the 1/r 2-potential

• DOI: 10.1007/bf01213405
• Publication Date: 2005-02-25T14:51:58Z
• Authors: Eric D'Hoker; Luc Vinet
• Keywords: Hamiltonian (control theory); Pauli exclusion principle; Self-adjoint operator

We examine the recently discovered dynamical OSp(1, 1) supersymmetry of the Pauli Hamiltonian for a spin 1/2 particle with gyromagnetic ratio 2, in the presence of a Dirac magnetic monopole. Using this symmetry and algebraic methods only, we construct the spectrum and obtain the wave functions. At all but the lowest angular momenta, the states transform under a single irreducible representation of OSp(1, 1). On the lowest angular momentum states, it is impossible to define self-adjoint supercharges, and the states transform under an irreducible representation of SO(2, 1) only. The Hamiltonian is not self-adjoint in thes-wave sector, but admits a one parameter family of self-adjoint extensions. The full SO(2, 1) algebra can be realized only for two specific values of the parameter.