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Discrete Dynamics in Nature and Society - Volume 4 2000, Issue 1, Pages 77-86

Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Ramat Aviv 69978, Israel

Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel

Received 21 December 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations classically in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.

Author: L. P. Horwitz and Y. Ashkenazy



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