Distinguished Self-Adjoint Extension of the Two-Body Dirac Operator with Coulomb Interaction

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...

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Veröffentlicht in:Annales Henri Poincaré 2019-07, Vol.20 (7), p.2407-2445
Hauptverfasser: Deckert, Dirk-André, Oelker, Martin
Format: Artikel
Sprache:eng
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Zusammenfassung: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 / π .
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-019-00802-6