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arXiv · hep-th/0602181

Supercharge Operator of Hidden Symmetry in the Dirac Equation

Tamari~T. Khachidze·Anzor~A. Khelashvili
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Abstract

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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Tamari~T. Khachidze, Anzor~A. Khelashvili. 2006-02-18. Supercharge Operator of Hidden Symmetry in the Dirac Equation. https://doi.org/10.1063/1.2435304

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