Self-Adjoint Extensions of Dirac Operator with Coulomb Potential

Abstract

In this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential $V(\vec{x})=\varphi (\vec{x})I_4$. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.

arXiv comment17 pages

References in corpus (3)

• Self-adjointness of Dirac operators via Hardy-Dirac inequalities
• Self-adjoint extensions of Dirac operators with Coulomb type singularity
• Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

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• Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations
• Self-adjointness in Quantum Mechanics: a pedagogical path
• Interior-Boundary Conditions for the Dirac Equation at Point Sources in 3 Dimensions
• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
• Creation Rate of Dirac Particles at a Point Source
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors