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On the contribution of the Coulomb singularity of arbitrary charge to the Dirac Hamiltonian
Author(s):
Jingbo
Xia
Journal:
Trans. Amer. Math. Soc.
351
(1999),
1989-2023.
MSC (1991):
Primary 47A10, 47F05, 81Q10, 81V45
Posted:
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:
10.1090/S0002-9947-99-02084-X
PII:
S 0002-9947(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
Posted:
January 26, 1999
Additional Notes:
Research supported in part by National Science Foundation grant DMS-9400600.
Copyright of article:
Copyright
1999,
American Mathematical Society
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