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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
Article
  • 21 Downloads

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 \(2/\pi \).

Notes

Acknowledgements

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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität MünchenMunichGermany

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