On twodimensional superpotentials: from classical Hamilton Jacobi theory to 2D supersymmetric quantum mechanics
Abstract
Superpotentials in {\cal N}=2 supersymmetric classical mechanics are no more than the Hamilton characteristic function of the HamiltonJacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are several superpotentials ruling HamiltonJacobi separable supersymmetric systems, with a number of degrees of freedom greater than 1. Here, we explore how supersymmetry and separability are entangled in the quantum version of this kind of system. We also show that the planar anisotropic harmonic oscillator and the two Newtonian centres of force problem admit two nonequivalent supersymmetric extensions with different ground states and Yukawa couplings.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2004
 DOI:
 10.1088/03054470/37/43/020
 arXiv:
 arXiv:hepth/0401054
 Bibcode:
 2004JPhA...3710323A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 14 pages, 2 figures, version to appear in J. Phys. A: Math. Gen