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 Coulomblike singular scalar potential V(X) = ϕ (x)I4. 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.
Self-adjoint extensions of dirac operator with coulomb potential / M. Gallone (SPRINGER INDAM SERIES). - In: Advances in Quantum Mechanics : Contemporary Trends and Open Problems / [a cura di] A. Michelangeli, G. Dell'Antonio. - [s.l] : Springer, 2017. - ISBN 9783319589039. - pp. 169-185 (( convegno INdAM International Meeting on Contemporary Trends in the Mathematics of Quantum Mechanics tenutosi a Roma nel 2016 [10.1007/978-3-319-58904-6_10].
Self-adjoint extensions of dirac operator with coulomb potential
M. Gallone
2017
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 Coulomblike singular scalar potential V(X) = ϕ (x)I4. 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.
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