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Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms

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Abstract

Some general results about perturbations of not-semibounded self-adjoint operators by quadratic forms are obtained. These are applied to obtain the distinguished self-adjoint extension for Dirac operators with singular potentials (including potentials dominated by the Coulomb potential withZ<137). The distinguished self-adjoint extension, is theunique self-adjoint extension, for which the wave functions in its domain possess finite mean kinetic energy. It is shown moreover that the essential spectrum of the distinguished extension is contained in the spectrum of the free Hamiltonian.

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  1. Institute of Atomic Physics, Bucharest, Romania

    G. Nenciu

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  1. G. Nenciu
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Communicated by W. Hunziker

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Nenciu, G. Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms. Commun.Math. Phys. 48, 235–247 (1976). https://doi.org/10.1007/BF01617872

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  • DOI: https://doi.org/10.1007/BF01617872

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