Comment on "Supersymmetry and Singular Potentials" by Das and Pernice [Nucl. Phys. B 561 (1999) 357]

TL;DR

This paper discusses a novel regularization method for singular potentials in supersymmetric quantum mechanics using a complex coordinate shift and PT-symmetric Hamiltonians, building on prior work by Das and Pernice.

Contribution

It introduces a natural regularization approach via an infinitesimal complex shift, mediated by a non-Hermitian PT-symmetric Hamiltonian, for singular potentials in supersymmetric quantum mechanics.

Findings

Regularization achieved through complex coordinate shift.

PT-symmetric Hamiltonian mediates the regularization.

Supports supersymmetric quantum mechanics with singular potentials.

Abstract

Witten's supersymmetric quantum mechanics may incorporate potentials with strong singularities after their appropriate regularization. This was proposed by Das and Pernice [Nucl. Phys. B 561 (1999) 357 and arXiv: hep-th/0207112]. We suggest that one of the most natural recipes of this type is generated by an infinitesimal complex shift of coordinates. The necessary regularization is then mediated by a non-Hermitian, PT symmetric intermediate Hamiltonian.