$\mathcal{N}$-FOLD PARASUPERSYMMETRY

Abstract

We find a new type of non-linear supersymmetries, called N -fold parasupersymmetry, which is a generalization of both N -fold supersymmetry and parasupersymmetry. We provide a general formulation of this new symmetry and then construct a second-order N -fold parasupersymmetric quantum system where all the components of N -fold parasupercharges are given by type A N -fold supercharges. We show that this system exactly reduces to the Rubakov-Spiridonov model when N = 1 and admits a generalized type C 2N -fold superalgebra. We conjecture the existence of other 'N -fold generalizations' such as N -fold fractional supersymmetry, N -fold orthosupersymmetry, and so on.

$\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS

“…We expect that we can formulate higher-order paraSUSY in quantum mechanical matrix models in a way such that the relations to N -fold SUSY in the scalar case remain intact in a matrix case. Extension of higher-order N -fold paraSUSY [30] to matrix systems would be also possible.…”

“…On the other hand, for non-trivial solutions the combination C 1i /C 0i :=C (i = 1, 2, 3) should not depend on the index i. Let us first consider the set of conditions (29) and (30). We find that the two combinations w 10 ×(29)+C 2 v 1 ×(30) and v 1 ×(29)+w 10 ×(30) are total differentials and thus are integrated respectively as 2w 10 w ′′ 10 − (w ′ 10 ) 2 − 2(w 10 ) 2 w ′ 10 + 4(w 10 ) 2 w 00 − (w 10 ) 4…”

${\mathcal N}$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS

“…We expect that we can formulate higher-order paraSUSY in quantum systems with reflections in a way such that the relations to N -fold SUSY in the case without reflections remain intact in the latter case. Extension of higherorder N -fold paraSUSY [26] to quantum systems with reflections would be also possible.…”