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] M. Arai, On essential selfadjointness, distinguished selfadjoint extension and essential spectrum of Dirac operators with matrix valued potentials, Publ. Res. Inst. Math. Sci. 19 (1983), 33-57. MR 700939 (85i:35106)
  • [2] A. O. Barut and J. Kraus, Solution of the Dirac equation with Coulomb and magnetic moment interactions, J. Math. Phys. 17 (1976), 506-508. MR 0411434 (53:15168)
  • [3] H. Behncke, The Dirac equation with an anomalous magnetic moment, Math. Z. 174 (1980), 213-225. MR 593820 (82g:81014)
  • [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 (1979), 171-176. MR 519923 (80k:81025)
  • [9] J. J. Landgren and P. A. Rejto, On a theorem of Jörgens and Chernoff concerning essential self-adjointness of Dirac operators, J. Reine Angew. Math. 332 (1981), 1-14. MR 603023 (82j:81020)
  • [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] H. Narnhofer, Acta Phys. Austriaca 40 (1974), 306-322. MR 0368660 (51:4901)
  • [12] E. Nelson, unpublished.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] M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press, New York, 1975. MR 0493420 (58:12429b)
  • [15] J. Weidmann, Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen, Math. Z. 119 (1971), 349-373. MR 0285758 (44:2975)
  • [16] H. Behncke, Dirac equation with an anomalous magnetic moment. II, Ordinary and Partial Differential Equations (W. N. Everitt and B. D. Sleeman, eds.), Lecture Notes in Math., Vol. 964, Springer, Berlin and New York, 1982, pp. 77-85. MR 693103 (84e:81011)

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