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Transactions of the American Mathematical Society

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

Author: Jingbo Xia
Journal: Trans. Amer. Math. Soc. 351 (1999), 1989-2023
MSC (1991): Primary 47A10, 47F05, 81Q10, 81V45
Published electronically: January 26, 1999
MathSciNet review: 1451618
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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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Additional Information

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214

Keywords: Dirac operator, spectrum, perturbation
Received by editor(s): January 15, 1996
Received by editor(s) in revised form: February 27, 1997
Published electronically: January 26, 1999
Additional Notes: Research supported in part by National Science Foundation grant DMS-9400600.
Article copyright: © Copyright 1999 American Mathematical Society