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Discrete spectrum of electromagnetic Dirac operators
Author(s):
Naohiro
Suzuki
Journal:
Proc. Amer. Math. Soc.
128
(2000),
819-825.
MSC (1991):
Primary 35P25;
Secondary 81Q10
Posted:
June 17, 1999
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Abstract:
We consider the Dirac operators with electromagnetic fields on 2-dimensional Euclidean space. We offer the sufficient conditions for electromagnetic fields that the associated Dirac operator has only discrete spectrum.
References:
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- P. R. Chernoff, Schrödinger and Dirac operators with singular potentials and hyperbolic equations, Pac. J. Math. 72 (1977), 361-382. MR 58:23150
- 2.
- Colin de Verdiere, L'asymptotique de Weyl pour les bouteilles magnétiques, Comm. Math. Phys. 105 (1986), 327-335. MR 87k:58273
- 3.
- A. Iwatsuka, Magnetic Schrödinger operators with compact resolvent, J. Math. Kyoto Univ. 26-3 (1986), 357- 374. MR 87j:35287
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- M. Reed and B. Simon, Methods of modern mathematical physics, II, Fourier Analysis, Self-adjointness, Academic Press, New York, 1975. MR 58:12429b
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- -, Methods of modern mathematical physics, IV, Analysis of Operators, Academic Press, New York, 1978. MR 58:12429c
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- B. Thaller, The Dirac equation, Springer-Verlag, Berlin/Heidelberg, 1992. MR 94k:81056
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Additional Information:
Naohiro
Suzuki
Affiliation:
49-9 Shinsakae, Shinden, Anjo, Aichi, 446-0061 Japan
Email:
nhsuzuki@cb3.so-net.or.jp
DOI:
10.1090/S0002-9939-99-05073-X
PII:
S 0002-9939(99)05073-X
Keywords:
Dirac operator,
discrete spectrum,
electromagnetic fields
Received by editor(s):
September 12, 1997
Received by editor(s) in revised form:
April 29, 1998
Posted:
June 17, 1999
Communicated by:
David R. Larson
Copyright of article:
Copyright
1999,
American Mathematical Society
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