Abstract

We show that the N = 2 superextended 1D quantum Dirac delta potential problem is characterized by the hidden nonlinear su (2 | 2) superunitary symmetry. The unexpected feature of this simple supersymmetric system is that it admits three different Z2-gradings, which produce a separation of 16 integrals of motion into three different sets of 8 bosonic and 8 fermionic operators. These three different graded sets of integrals generate two different nonlinear, deformed forms of su (2 | 2), in which the Hamiltonian plays a role of a multiplicative central charge. On the ground state, the nonlinear superalgebra is reduced to the two distinct 2D Euclidean analogs of a superextended Poincaré algebra used earlier in the literature for investigation of spontaneous supersymmetry breaking. We indicate that the observed exotic supersymmetric structure with three different Z2-gradings can be useful for the search of hidden symmetries in some other quantum systems, in particular, related to the Lamé equation. © 2007 Elsevier B.V. All rights reserved.