On two-dimensional superpotentials: from classical Hamilton-Jacobi theory to 2D supersymmetric quantum mechanics

Abstract

Superpotentials in $\mathcal{N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are several superpotentials ruling Hamilton-Jacobi separable supersymmetric systems, with a number of degrees of freedom greater than one. 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 centers of force problem admit two non-equivalent supersymmetric extensions with different ground states and Yukawa couplings.

arXiv comment14 pages, 2 figures, version to appear in J. Phys. A: Math. Gen

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Cited by in corpus (6)

• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
• Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
• On the Supersymmetric Spectra of two Planar Integrable Quantum Systems
• Canonical D = 1 supergravity framework for FLRW cosmology
• Factorization of supersymmetric Hamiltonians in curvilinear coordinates
• Supersymmetry and Integrability in Planar Mechanical Systems