Abstract
The geometric-optics theory for the Dirac equation is derived using a procedure developed for the description of electromagnetic waves in inhomogeneous plasmas. This semiclassical description of relativistic electrons permits simple estimates of the magnitude and relevance of quantum corrections to the classical particle dynamics which can be used to assess the validity of the classical treatment of relativistic electron beams in a variety of applications. Moreover, these results correct several errors in the literature and are presented in a form which is easily solved, numerically, using straightforward modifications of existing ray-tracing codes for electromagnetic radiation.
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