Covariant generalization of the Zitterbewegung of the electron and its SO(4,2) and SO(3,2) internal algebras

A. O. Barut; W. Thacker

doi:10.1103/PhysRevD.31.1386

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Covariant generalization of the Zitterbewegung of the electron and its SO(4,2) and SO(3,2) internal algebras

A. O. Barut and W. Thacker

Department of Physics, University of Colorado, Boulder, Colorado 80309

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Phys. Rev. D 31, 1386 – Published 15 March, 1985

DOI: https://doi.org/10.1103/PhysRevD.31.1386

Abstract

The internal geometry of the Dirac electron is studied in a proper-time formalism with $γ^{0}$ -Hermitian operators. We solve the Heisenberg equations, separate external and internal coordinates, and identify the SO(3,2) internal algebra as the projection of an SO(3,3) geometry to the hyperplane (perpendicular to the center-of-mass momentum) where the Zitterbewegung takes place. We also give covariant intrinsic-spin and magnetic-moment operators. The system can be generalized to a larger system with the internal geometry SO(4,2) with the inclusion of dynamical variables $γ^{5}$ and i $γ^{5}$ $γ^{μ}$ . The resultant internal algebras have higher-dimensional representations generalizing the Dirac electron to multifermion states.

References (16)

A. O. Barut and A. J. Bracken, Phys. Rev. D 23, 2454 (1981).
J. A. DeVos and J. Hilgevoord, Nucl. Phys. B 1, 494 (1967).
M. Bakri, Nuovo Cimento 51 A, 864 (1967); Nucl. Phys. B 12, 341 (1969).
See also, L. P. Horwitz and C. Piron, Helv. Phys. Acta 46, 316 (1973).
H. C. Corben, Phys. Rev. 121, 1833 (1961).
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W. Drechsler, Fortsch. Phys. 27, 489 (1979).
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A. O. Barut, in Quantum Optics, Relativity and Theory of Measurement, edited by P. Meystre (Plenum, New York, 1983), p. 155.
A. O. Barut and N. Zanghi, Phys. Rev. Lett. 52, 2009 (1984).
R. R. Aldinger et al., Phys. Rev. D 28, 3020 (1983); A. Bohm et al., ibid. 28, 3030 (1983).
A. O. Barut, Phys. Rev. Lett. 20, 893 (1968).
A. O. Barut, A. J. Bracken, and W. Thacker, Lett. Math. Phys. (to be published).
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A. O. Barut and A. J. Bracken, Phys. Rev. D 24, 3333 (1981).

[c1] A. O. Barut and A. J. Bracken, Phys. Rev. D 23, 2454 (1981).

[c2] J. A. DeVos and J. Hilgevoord, Nucl. Phys. B 1, 494 (1967).

[c3] M. Bakri, Nuovo Cimento 51 A, 864 (1967); Nucl. Phys. B 12, 341 (1969).

[c4] See also, L. P. Horwitz and C. Piron, Helv. Phys. Acta 46, 316 (1973).

[c5] H. C. Corben, Phys. Rev. 121, 1833 (1961).

[c6] G. Szamosi, Nuovo Cimento 20, 1090 (1961).

[c7] W. Drechsler, Fortsch. Phys. 27, 489 (1979).

[c8] J. R. Ellis, J. Phys. A 14, 2917 (1981).

[c9] A. O. Barut, in Quantum Optics, Relativity and Theory of Measurement, edited by P. Meystre (Plenum, New York, 1983), p. 155.

[c10] A. O. Barut and N. Zanghi, Phys. Rev. Lett. 52, 2009 (1984).

[c11] R. R. Aldinger et al., Phys. Rev. D 28, 3020 (1983); A. Bohm et al., ibid. 28, 3030 (1983).

[c12] A. O. Barut, Phys. Rev. Lett. 20, 893 (1968).

[c13] A. O. Barut, A. J. Bracken, and W. Thacker, Lett. Math. Phys. (to be published).

[c14] A. O. Barut, in Groups, Systems, and Many-Body Physics, edited by P. Kramer (Vieweg, Braunschweig, 1980), Chap. VI.

[c15] A. O. Barut and G. Bornzin, J. Math. Phys. 15, 1000 (1974).

[c16] A. O. Barut and A. J. Bracken, Phys. Rev. D 24, 3333 (1981).

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Covariant generalization of the Zitterbewegung of the electron and its SO(4,2) and SO(3,2) internal algebras

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