Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
| Autor: | Correa, Francisco, Falomir, Horacio, Jakubsky, Vit, Plyushchay, Mikhail S. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Annals Phys.325:2653-2667,2010 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aop.2010.06.005 |
| Popis: | The quantum nonrelativistic spin-1/2 planar systems in the presence of a perpendicular magnetic field are known to possess the N=2 supersymmetry. We consider such a system in the field of a magnetic vortex, and find that there are just two self-adjoint extensions of the Hamiltonian that are compatible with the standard N=2 supersymmetry. We show that only in these two cases one of the subsystems coincides with the original spinless Aharonov-Bohm model and comes accompanied by the super-partner Hamiltonian which allows a singular behavior of the wave functions. We find a family of additional, nonlocal integrals of motion and treat them together with local supercharges in the unifying framework of the tri-supersymmetry. The inclusion of the dynamical conformal symmetries leads to an infinitely generated superalgebra, that contains several representations of the superconformal osp(2|2) symmetry. We present the application of the results in the framework of the two-body model of identical anyons. The nontrivial contact interaction and the emerging N=2 linear and nonlinear supersymmetries of the anyons are discussed. Comment: 18 pages, 1 figure, published version |
| Databáze: | arXiv |
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