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

DOI:
https://doi.org/10.1090/S0002-9947-99-02084-X

Published electronically:
January 26, 1999

MathSciNet review:
1451618

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Abstract: We study the self-adjoint extensions of the Dirac operator , where the electrical potential contains a Coulomb singularity of arbitrary charge and the magnetic potential is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form where 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

Email:
jxia@acsu.buffalo.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02084-X

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