Abstract
A covariant expression is given for the self-action of the electron. By postulating that the self-action adopts an extremum, the equation for the derivative of the four-dimensional vector potential with respect to the universal time is obtained by applying the calculus of variation to the action integral. By considering the electron as a moving point-like particle and by employing the four-dimensional Green formalism, we express the four-dimensional vector potential of the moving electron as a loop integral which can be solved analytically. The resulting electromagnetic field consists of the accompanying field attached to the electron and the radiation field resulting from the acceleration.
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References
H. Rose, in Advances in Imaging and Electron Physics, vol. 132, ed. by P.W. Hawkes (Academic, London, 2004), pp. 247–285
J. D. Jackson, Classical Electrodynamics, 2nd edn. (Wiley, New York, 1975)
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© 2012 Springer-Verlag Berlin Heidelberg
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Rose, H. (2012). Electron Self-Action. In: Geometrical Charged-Particle Optics. Springer Series in Optical Sciences, vol 142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32119-1_15
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DOI: https://doi.org/10.1007/978-3-642-32119-1_15
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