On the contribution of the Coulomb singularity of arbitrary charge to the Dirac Hamiltonian

Xia, Jingbo

doi:10.1090/S0002-9947-99-02084-X

On the contribution of the Coulomb singularity of arbitrary charge to the Dirac Hamiltonian
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by Jingbo Xia PDF

Trans. Amer. Math. Soc. 351 (1999), 1989-2023 Request permission

Abstract:

We study the self-adjoint extensions of the Dirac operator $\alpha \cdot (p - B) + \mu _{0}\beta - W$, where the electrical potential $W$ contains a Coulomb singularity of arbitrary charge and the magnetic potential $B$ is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form $v(r)/r$ where $v$ has a limit at 0, then, for any self-adjoint extension of the Dirac operator, removing the singularity results in a Hilbert-Schmidt perturbation of its resolvent.

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