Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems

TL;DR

This paper investigates a superspace Schrödinger equation with osp(D|2n) symmetry, constructs a related dynamical superalgebra, and analyzes bound states as irreducible modules to determine energy spectra and eigenspaces.

Contribution

It introduces a supersymmetric quantum Kepler problem in superspace and explicitly constructs the associated dynamical superalgebra and its irreducible modules.

Findings

Explicit osp(2,D+1|2n) dynamical supersymmetry constructed

Bound states form irreducible highest weight modules

Energy eigenvalues and eigenspaces determined

Abstract

A Schroedinger type equation on the superspace R^{D|2n} is studied, which involves a potential inversely proportional to the negative of the osp(D|2n) invariant "distance" away from the origin. An osp(2,D+1|2n) dynamical supersymmetry for the system is explicitly constructed, and the bound states of the system are shown to form an irreducible highest weight module for this superalgebra. A thorough understanding of the structure of the irreducible module is obtained. This in particular enables the determination of the energy eigenvalues and the corresponding eigenspaces as well as their respective dimensions.