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

TL;DR

This paper establishes a unique self-adjoint extension for the two-body Dirac operator with Coulomb interaction, ensuring well-defined quantum dynamics under certain coupling bounds.

Contribution

It introduces a distinguished self-adjoint extension for the two-body Dirac operator with Coulomb potential, based on finite potential energy criteria.

Findings

Existence of a unique self-adjoint extension under coupling bounds.

Extension applies to both repulsive and attractive interactions.

Technical bound on coupling constant for Coulomb case is established.

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 $2/\pi$.