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Prog. Theor. Phys. Vol. 39 No. 2 (1968) pp. 372-393

[ Full Text PDF : FREE ACCESS (1197K) ]

The Frenkel-Kramers Model and the Zitterbewegung in the Extended Heisenberg Picture of the Dirac Electron

Hisaiti Yamasaki

Kyusyu Dental College, Kitakyusyu

(Received August 10, 1967)

Abstract:

With respect to the principal operators including the sixteen 4-4 matrices of the Dirac electron, two covariant forms of the extended Heisenberg picture can be presented with the “two covariant Hamiltonians HI and HII” of the first and second order, respectively. One form with HII involving the proper electromagnetic moment corresponds perfectly to the Frenkel-Kramers model which was recently treated by the author; the other form with HI containing the Zitterbewegung corresponds partly to the so-called Weyssenhoff-like model. That an amalgamation of the former form and the Zitterbewegung brings immediately the latter is explicitly shown by virtue of a decomposition of the operator of the Dirac electron into two corresponding parts. This decomposition is derived from the author's extension of the Feynman-Bunge-Corben formula for the position operator of the electron and, in case without external fields, it corresponds to the covariant form of the so-called `gerade-ungerade' decomposition.
In the case of the free state mixed with positive and negative energy, the Zitterbewegung of operators derived from HI can properly be realized by the expectation values of the operators. In this process, the author's complex hyperbolic metric of velocity which represents a new negative energy state plays an essential role.
These results give an important clue to solve the puzzling problem of the construction of a consistent classical model for the Dirac electron, and also may be useful for investigation of `internal structure' of elementary particles as well as their spin.


URL : http://ptp.ipap.jp/link?PTP/39/372/
DOI : 10.1143/PTP.39.372

[ Full Text PDF : FREE ACCESS (1197K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 42 No. 2 (1969) pp. 234-244 :
    Reformulation of the Frenkel-Kramers Model Including the Thomas Precession with the Velocity Metric
    Hisaiti Yamasaki

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