Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On the selfadjointness of Dirac operators with anomalous magnetic moment

Authors: F. Gesztesy, B. Simon and B. Thaller
Journal: Proc. Amer. Math. Soc. 94 (1985), 115-118
MSC: Primary 35P05; Secondary 47F05, 81C10
MathSciNet review: 781067
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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,
  • [2] 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 0411434,
  • [3] Horst Behncke, The Dirac equation with an anomalous magnetic moment, Math. Z. 174 (1980), no. 3, 213–225. MR 593820,
  • [4] -, Spectral properties of the Dirac equation with anomalous magnetic moment, preprint.
  • [5] H. Frauenfelder and E. M. Henley, Subatomic physics, Prentice-Hall, Englewood Cliffs, N. J., 1974.
  • [6] W. Greiner (ed.), Quantum electrodynamics of strong fields, Vol. B80, Nato Advanced Study Institute Series, Plenum, 1983.
  • [7] T. Kato, Perturbation theory for linear operators, 2nd ed., Springer-Verlag, Berlin and New York, 1980.
  • [8] 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
  • [9] 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,
  • [10] B. Müller and W. Greiner, The physics of strong fields in quantum electrodynamics and general relativity, Acta Phys. Austriaca Suppl. 18 (1977), 153-384.
  • [11] Heide Narnhofer, Quantum theory for 1/𝑟²-potentials, Acta Phys. Austriaca 40 (1974), 306–322. MR 0368660
  • [12] E. Nelson, unpublished.
  • [13] W. Pauli, Die allgemeinen Prinzipien der Wellenmechanik, Encyclopedia of Physics V/1 (S. Flügge, ed.), Springer, Berlin and New York, 1958.
  • [14] Michael Reed and Barry Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0493420
  • [15] Joachim Weidmann, Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen, Math. Z. 119 (1971), 349–373 (German). MR 0285758,
  • [16] 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

Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society