Dirac delta potential problem

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 supersymmetry admits three distinct Z2-gradings, that results in a separation of 16 integrals of motion into different sets of 8 bosonic and 8 fermionic operators generating two 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 by Gershun and Tkach for investigation of spontaneous supersymmetry breaking.