Supercharge Operator of Hidden Symmetry in the Dirac Equation

Details Supercharge Operator of Hidden Symmetry in the Dirac Equation Supercharge Operator of Hidden Symmetry in the Dirac Equation

2006-02-18

arxiv.org/abs/hep-th/0602181v1

GESJ Phys.1:88-97,2006; AIP Conf.Proc.881:279-284,2007

Physics

High Energy Physics

High Energy Physics - Theory

3 pages

Scientific paper

10.1063/1.2435304

As is known, the so-called Dirac $K$-operator commutes with the Dirac Hamiltonian for arbitrary central potential $V(r)$. Therefore the spectrum is degenerate with respect to two signs of its eigenvalues. This degeneracy may be described by some operator, which anticommutes with $K$. If this operator commutes with the Dirac Hamiltonian at the same time, then it establishes new symmetry, which is Witten's supersymmetry. We construct the general anticommuting with $K$ operator, which under the requirement of this symmetry unambiguously select the Coulomb potential. In this particular case our operator coincides with that, introduced by Johnson and Lippmann many years ago.

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