Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem

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 ${\mathbb{Z}}_2$-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 ${\mathbb{Z}}_2$-gradings can be useful for the search of hidden symmetries in some other quantum systems, in particular, related to the Lamé equation.

11 pages; comments and refs. added, version published in PLB

References in corpus (4)

• Hidden supersymmetry in quantum bosonic systems
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• A new effective mass Hamiltonian and associated Lame equation: bound states
• New supersymmetric partners for the associated Lame potentials

Cited by in corpus (6)

• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• BRST structure of non-linear superalgebras