Abstract
The existence of zitterbewegung of particles with higher spins (s≥1) is proved. The investigation is based on the idea of Curie, Jordan, and Sudarshan that there are two aspects of relativistic invariance and also on the determination of the dynamical variables that describe systems with arbitrary spin obtained by Jordan and Mukunda. A number of new paradoxical properties of zitterbewegung unknown in Dirac theory is revealed. For example, particles with high spins (s≥1) can have a velocity greater than light. It is shown in a general form that elimination of zitterbewegung in all directions of space, or even only in a plane, is impossible. There can be only partial liquidation of zitterbewegung, in one of the directions of space, and then only at the price of violation of relativistic invariance of the theory. Finally, it is suggested that the paradoxical properties of zitterbewegung can be understood by redefining the momentum and mass operators. In this way, a connection between zitterbewgung and tachyons is established.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–60, April, 1975.
We should like to take this opportunity of thanking Prof. D. D. Ivanenko and Prof. Ya. P. Terletskii for enabling us to discuss our results at the theoretical physics seminars at the M. V. Lomonosov Moscow State University at the Patrice Lumumba University of People's Friendship.
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Izmailov, S.V., Levin, E.S. Zitterbewegung of particles with arbitrary spin. Soviet Physics Journal 18, 481–488 (1975). https://doi.org/10.1007/BF01093237
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DOI: https://doi.org/10.1007/BF01093237