Coulomb Potential and Witten Superalgebra

Details Coulomb Potential and Witten Superalgebra Coulomb Potential and Witten Superalgebra

2009-02-06

arxiv.org/abs/0902.1122v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

The additional hidden symmetry of the Coulomb-Kepler problem is reviewed in classical as well as in quantum mechanics. The main purpose is to elucidate the role of this kind of symmetries in the reduction of physical problems, to show algebraic possibilities of derivation of spectra. The original results are presented also. They are hidden symmetries in the Dirac equation, where it is shown that the requirement of invariance of the Dirac Hamiltonian under some kind of Witten's superalgebra, picks out the Coulomb potential only. The problem in the arbitrary higher dimensions is also considered. It is derived that the traditional view on the Coulomb potential is to be changed in the context of N=2 supersymmetry

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