The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics

Abstract

The structure of supersymmetry is analyzed systematically in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional $\mathcal{P}\mathcal{T}$ 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.

15 pages, some explanations included, references added

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Non-commutative Supersymmetric Quantum Mechanics
• Supersymmetric Biorthogonal Quantum Systems

Cited by in corpus (4)

• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Supersymmetry, shape invariance and the Legendre equations
• Supersymmetry, shape invariance and the hypergeometric equation