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Rigorous theoretical arguments for suppression of the Lamb shift. (English) Zbl 1308.81078

Summary: The main purpose is to elucidate the role of the hidden symmetry of the Dirac-Coulomb problem and to show algebraic possibilities for derivation of spectra. 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. It follows that the traditional view on the Coulomb potential is to be changed in the context of \(N = 2\) supersymmetry.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
17A70 Superalgebras
81V45 Atomic physics
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