Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-07-10
Phys.Lett.B659:746-753,2008
Physics
High Energy Physics
High Energy Physics - Theory
11 pages; comments and refs. added, version published in PLB
Scientific paper
10.1016/j.physletb.2007.11.046
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 Poincar\'e 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 Lam\'e equation.
Correa Francisco
Nieto Luis Miguel
Plyushchay Mikhail S.
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