Abstract
It is shown that for a large class of potential problems in the Dirac equation the positive and negative energy solutions do not mix even in the strong coupling limit We prove that this property, which implies a stability of the Dirac sea, is connected to the presence of superalgebra operators in the Dirac equation. The exact and closed form for the Foldy-Wouthuysen Hamiltonian which is used to prove this property are given. The potentials include the Dirac oscillator, the uniform time-independent magnetic field and the odd potentials and its nonabelian generalizations.
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