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

DOI10.1016/J.PHYSLETB.2007.11.046zbMATH Open1246.81060arXiv0707.1393OpenAlexW2086234391MaRDI QIDQ446956

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Publication date: 8 September 2012

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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 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.

Full work available at URL: https://arxiv.org/abs/0707.1393

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