Proceedings of the Japan Academy, Series A, Mathematical Sciences

Essential self-adjointness of Dirac operators with a variable mass term

Hubert Kalf and Osanobu Yamada

Full-text: Open access

Abstract

In this paper we study the essential self-adjointness of Dirac operators with a variable mass term $m(x)$ and an electric potential $V(x)$. We are mainly interested in the local singularities of $m(x)$ and $V(x)$. We can treat singularities of $m(x)$ and $V(x)$ which are stronger than those of Coulomb potentials.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 2 (2000), 13-15.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393580

Digital Object Identifier
doi:10.3792/pjaa.76.13

Mathematical Reviews number (MathSciNet)
MR1752816

Zentralblatt MATH identifier
0952.35113

Subjects
Primary: 35P05: General topics in linear spectral theory 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords
Essential self-adjointness Dirac operator self-adjoint operator singular potential

Citation

Kalf, Hubert; Yamada, Osanobu. Essential self-adjointness of Dirac operators with a variable mass term. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 2, 13--15. doi:10.3792/pjaa.76.13. https://projecteuclid.org/euclid.pja/1148393580


Export citation

References

  • Arai, M.: On essential selfadjointness, distinguished selfadjoint extension and essential spectrum of Dirac operators with matrix valued potentials. Publ. Res. Inst. Math. Sci., Kyoto Univ., 19, 33–57 (1983).
  • Arnold, V. Kalf, H. and Schneider, A.: Separated Dirac operators and asymptotically constant linear systems. Math. Proc. Camb. Phil. Sco., 121, 141–146 (1997).
  • Behncke, H.: The Dirac Equation with an anomalous magnetic moment. Math. Z., 174, 213–225 (1980).
  • Kalf, H.: Essential self-adjointness of Dirac operators under an integral condition on the potential. Letters in Math. Phys., 44, 225–232 (1998).
  • Kato, T.: Schrödinger operators with singular potentials. Israel J. Math., 13, 135–148 (1972).
  • Schmincke, U.-W.: Essential selfadjointness of Dirac operators with a strongly singular potential. Math. Z., 126, 71–81 (1972).
  • Schmidt, K. M. and Yamada, O.: Spherically symmetric Dirac operators with variable mass and potentials infinite at infinity. Publ. Res. Inst. Math. Sci., Kyoto Univ., 34, 211–227 (1998).
  • Vasconcelos, J.: Dirac particle in a scalar Coulomb field. Revista Brasileira de Fisica, 1, 441–450 (1971).
  • Yamada, O.: A remark on the essential self-adjointness of Dirac operators. Proc. Japan Acad., 62A, 327–330 (1986).
  • Yamada, O.: On the spectrum of Dirac operators with the unbounded potential at infinity. Hokkaido Math. J., 26, 439–449 (1997).
  • Yosida, K.: Functional Analysis. Springer, Berlin-Heidelberg-New York (1965).