Anti-PT Transformations and Complex PT-Symmetric Superpartners

A quantum mechanical system with unbroken super-and parity-time (PT)-symmetry is derived and analyzed. Here, we propose a new formalism to construct the complex PT-symmetric superpartners by extending the additive shape invariant potentials to the complex domain. The probabilistic interpretation of a PT-symmetric quantum theory is correlated with the calculation of a new linear operator called the C operator, instead of complex conjugation in conventional quantum mechanics. At the present work, we introduce an anti-PT (A PT) conjugation to redefine a new version of the inner product without any additional considerations. This PT-supersymmetric quantum mechanics, satisfies essential requirements such as completeness, orthonormality as well as probabilistic interpretation.