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

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 $2/\pi$.

References in corpus (5)

• Self-adjointness of Dirac operators via Hardy-Dirac inequalities
• Self-adjoint extensions of Dirac operators with Coulomb type singularity
• Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei
• Stability of atoms in the Brown-Ravenhall model
• Self-Adjoint Extensions of Dirac Operator with Coulomb Potential

Cited by in corpus (4)

• The Scott correction in Dirac-Fock theory
• Self-adjointness in Quantum Mechanics: a pedagogical path
• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors