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CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C

B. Bagchi·A. Banerjee·E. Caliceti·F. Cannata·H. B. Geyer·C. Quesne·M. Znojil
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Abstract

A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. The integrability of intertwining relations proves to match the closure of nonlinear SUSY algebra. In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric.

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B. Bagchi, A. Banerjee, E. Caliceti, F. Cannata, H. B. Geyer, C. Quesne, M. Znojil. 2004-12-18. CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C. https://doi.org/10.1142/s0217751x05022901

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