N-fold Supersymmetry in Quantum Mechanics - General Formalism -

Details N-fold Supersymmetry in Quantum Mechanics - General Formalism - N-fold Supersymmetry in Quantum Mechanics - General Formalism -

2001-06-07

arxiv.org/abs/quant-ph/0106037v3

Nucl.Phys. B619 (2001) 105-127

Physics

Quantum Physics

25 pages

Scientific paper

10.1016/S0550-3213(01)00516-8

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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