The structure of supersymmetry in ${\cal PT}$ symmetric quantum mechanics

TL;DR

This paper systematically explores the structure of supersymmetry in PT-symmetric quantum mechanics, revealing richer structures than in conventional Hermitian systems and extending these concepts to higher dimensions and shape invariant potentials.

Contribution

It provides a detailed analysis of supersymmetric structures in PT-symmetric quantum theories, highlighting their complexity and generalizing to higher dimensions and specific potential classes.

Findings

Richer supersymmetric structures in PT-symmetric systems

Extension to higher-dimensional theories

Generalization to shape invariant potentials

Abstract

The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.