English

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

Mathematical Physics 2019-07-24 v1 math.MP

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/π2/\pi.

Keywords

Cite

@article{arxiv.1805.09634,
  title  = {Distinguished self-adjoint extension of the two-body Dirac operator with Coulomb interaction},
  author = {Dirk-André Deckert and Martin Oelker},
  journal= {arXiv preprint arXiv:1805.09634},
  year   = {2019}
}