Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the selfadjointness of Dirac operators with anomalous magnetic moment
HTML articles powered by AMS MathViewer

by F. Gesztesy, B. Simon and B. Thaller PDF
Proc. Amer. Math. Soc. 94 (1985), 115-118 Request permission

Abstract:

We provide a new proof of Behncke’s remarkable result that the Coulombic Dirac equation with nonzero anomalous magnetic moment is essentially selfadjoint (on $C_{00}^\infty {({R^3})^4}$) for any value of the Coulomb charge.
References
  • Masaharu Arai, On essential selfadjointness, distinguished selfadjoint extension and essential spectrum of Dirac operators with matrix valued potentials, Publ. Res. Inst. Math. Sci. 19 (1983), no. 1, 33–57. MR 700939, DOI 10.2977/prims/1195182974
  • A. O. Barut and J. Kraus, Solution of the Dirac equation with Coulomb and magnetic moment interactions, J. Mathematical Phys. 17 (1976), no. 4, 506–508. MR 411434, DOI 10.1063/1.522932
  • Horst Behncke, The Dirac equation with an anomalous magnetic moment, Math. Z. 174 (1980), no. 3, 213–225. MR 593820, DOI 10.1007/BF01161410
    • —, Spectral properties of the Dirac equation with anomalous magnetic moment, preprint. H. Frauenfelder and E. M. Henley, Subatomic physics, Prentice-Hall, Englewood Cliffs, N. J., 1974. W. Greiner (ed.), Quantum electrodynamics of strong fields, Vol. B80, Nato Advanced Study Institute Series, Plenum, 1983. T. Kato, Perturbation theory for linear operators, 2nd ed., Springer-Verlag, Berlin and New York, 1980.
  • M. Klaus and R. Wüst, Characterization and uniqueness of distinguished selfadjoint extensions of Dirac operators, Comm. Math. Phys. 64 (1978/79), no. 2, 171–176. MR 519923
  • J. J. Landgren and P. A. Rejto, On a theorem of Jörgens and Chernoff concerning essential selfadjointness of Dirac operators, J. Reine Angew. Math. 322 (1981), 1–14. MR 603023, DOI 10.1515/crll.1981.322.1
    • B. Müller and W. Greiner, The physics of strong fields in quantum electrodynamics and general relativity, Acta Phys. Austriaca Suppl. 18 (1977), 153-384.
  • Heide Narnhofer, Quantum theory for $1/r^{2}$-potentials, Acta Phys. Austriaca 40 (1974), 306–322. MR 368660
    • E. Nelson, unpublished. W. Pauli, Die allgemeinen Prinzipien der Wellenmechanik, Encyclopedia of Physics V/1 (S. Flügge, ed.), Springer, Berlin and New York, 1958.
  • Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
  • Joachim Weidmann, Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen, Math. Z. 119 (1971), 349–373 (German). MR 285758, DOI 10.1007/BF01109887
  • Horst Behncke, The Dirac equation with an anomalous magnetic moment. II, Ordinary and partial differential equations (Dundee, 1982) Lecture Notes in Math., vol. 964, Springer, Berlin-New York, 1982, pp. 77–85. MR 693103
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P05, 47F05, 81C10
  • Retrieve articles in all journals with MSC: 35P05, 47F05, 81C10
Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 115-118
  • MSC: Primary 35P05; Secondary 47F05, 81C10
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0781067-X
  • MathSciNet review: 781067