Annales Henri Poincaré

, Volume 20, Issue 7, pp 2407–2445 | Cite as

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

  • Dirk-André Deckert
  • Martin OelkerEmail author


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 \(2/\pi \).



We gratefully acknowledge fruitful discussions with Detlef Dürr and Martin Kolb. Also, we want to thank Jan Dereziński, Hubert Kalf, Jérémy Sok and Julien Sabin for their valuable comments.


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Authors and Affiliations

  1. 1.Mathematisches Institut der Universität MünchenMunichGermany

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