Parc de Grandmont, F-37200 TOURS (France)
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چکیده
Dynamical (super)symmetries of monopoles and vortices (1) Abstract. The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, no smooth Runge-Lenz vector can exist; there is, however, a spectrum-generating conformal o(2, 1) dynamical symmetry that extends into osp(1/1) or osp(1/2) for spin 1/2 particles. Self-dual 't Hooft-Polyakov-type monopoles admit an su(2/2) dy-namical supersymmetry algebra, which allows us to reduce the fluctuation equation to the spin zero case. For large r the system reduces to a Dirac monopole plus an suitable inverse-square potential considered before by McIntosh and Cisneros, and by Zwanziger in the spin 0 case, and to the 'dyon' of D'Hoker and Vinet for spin 1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a 'helicity-supersymmetry' analogous to the one Biedenharn found in the relativistic Kepler problem. Similar results hold for the Kaluza-Klein monopole of Gross-Perry-Sorkin. For the magnetic vortex, the N = 2 supersymmetry of the Pauli Hamiltonian in a static magnetic field in the plane combines with the o(2) × o(2, 1) bosonic symmetry into an o(2) × osp(1/2) dynamical superalgebra.
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تاریخ انتشار 2005