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arXiv · 1805.09634

Distinguished self-adjoint extension of the two-body Dirac operator with Coulomb interaction

Dirk-André Deckert·Martin Oelker
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Abstract

We study the two-body Dirac operator in a bounded external field and for a class of unbounded pair-interaction potentials, both repulsive and attractive, including the Coulomb type. Provided the coupling constant of the pair-interaction fulfills a certain bound, we prove existence of a self-adjoint extension of this operator which is uniquely distinguished by means of finite potential energy. In the case of Coulomb interaction, we require as a technical assumption the coupling constant to be bounded by $2/\pi$.

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Dirk-André Deckert, Martin Oelker. 2018-05-24. Distinguished self-adjoint extension of the two-body Dirac operator with Coulomb interaction. https://doi.org/10.1007/s00023-019-00802-6

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