Exact supersymmetry in the relativistic hydrogen atom in general dimensions -- supercharge and the generalized Johnson-Lippmann operator

Abstract

A Dirac particle in general dimensions moving in a 1/r potential is shown to have an exact N = 2 supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2))in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.

4 pages, 1 figure

References in corpus (2)

• Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions
• Exact solutions to the Dirac equation for a Coulomb potential in $D+1$ dimensions

Cited by in corpus (13)

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• Superintegrable systems with spin induced by coalgebra symmetry
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• SO(4) symmetry in the relativistic hydrogen atom
• su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions
• Algebra of the spinor invariants and the relativistic hydrogen atom
• Dirac eigenvalues for a softcore Coulomb potential in d dimensions
• On hydrogen-like bound states in $\mathcal{N}=4$ super Yang-Mills
• Algebraic Solution of the Supersymmetric Hydrogen Atom
• On the supersymmetry of the Dirac-Kepler problem plus a Coulomb-type scalar potential in D+1 dimensions and the generalized Lippmann-Johnson operator
• $SU(1,1)$ coherent states for Dirac-Kepler-Coulomb problem in $D+1$ dimensions with scalar and vector potentials
• Dynamical symmetry in a minimal dimeric complex