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Zbl 1193.81020
Hestenes, David
Zitterbewegung in quantum mechanics. (English)
[J] Found. Phys. 40, No. 1, 1-54 (2010). ISSN 0015-9018; ISSN 1572-9516/e

This interesting paper contains a research program investigating implications of the real Dirac equation for the interpretation and extension of quantum mechanics. The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with some features inherent in the well known Dirac equation. The author discusses a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. This model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency. The possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment. An interesting conclusion is that the relation of the zitterbewegung particle model to the Dirac equation can be considered from two different perspectives. On the one hand, it can be regarded as a ``quasiclassical" approximation that embodies structural features of the Dirac equation in a convenient form. On the other hand, it can be regarded as formulating fundamental properties of the electron that are manifested in the Dirac equation in some kind of average form.
[Dimitar A. Kolev (Sofia)]

MSC 2000:: *81Q05 Closed and approximate solutions to quantum-mechanical equations
70H40 Relativistic dynamics

Keywords: Zitterbewegung; geometric algebra; electron channeling; de Broglie frequency

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