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N-fold Supersymmetry in Quantum Mechanics - General Formalism -

Hideaki Aoyama·Masatoshi Sato·Toshiaki Tanaka
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Abstract

We report general properties of N-fold supersymmetry in one-dimensional quantum mechanics. N-fold supersymmetry is characterized by supercharges which are N-th polynomials of momentum. Relations between the anti-commutator of the supercharges and the Hamiltonian, the spectra, the Witten index, the non-renormalization theorems and the quasi-solvability are examined. We also present further investigation about a particular class of N-fold supersymmetric models which we dubbed type A. Algebraic equations which determine a part of spectra of type A models are presented, and the non-renormalization theorem are generalized. Finally, we present a possible generalization of N-fold supersymmetry in multi-dimensional quantum mechanics.

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Hideaki Aoyama, Masatoshi Sato, Toshiaki Tanaka. 2001-10-03. N-fold Supersymmetry in Quantum Mechanics - General Formalism -. https://doi.org/10.1016/s0550-3213(01)00516-8

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