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

Deckert, Dirk-Andre und Oelker, Martin (2019): Distinguished Self-Adjoint Extension of the Two-Body Dirac Operator with Coulomb Interaction. In: Annales Henri Poincare, Vol. 20, No. 7: pp. 2407-2445

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1424-0637
• Language: English