Coherence and Quantum Optics pp 509-521 | Cite as

# On the Theory of Radiating Electrons

Conference paper

## Abstract

In 1938 Dirac[1] showed that the self force on a point electron could be calculated in a consistent manner by assuming that it was due to just part of the field of the electron. Thus by splitting the field into two parts, a radiation field, which gave rise to the self force, and a bound field containing the diverging part of the field, he derived the Lorentz-Dirac equation governing the motion of the electron in an electromagnetic field. We discuss how this theory and the Lorentz-Dirac equation may be derived for each particle of a system of particles using the principle of least action from the action integral,

$${\text{I = }}\int {{{\text{d}}^4}{\text{x}}} \left\{ { - \frac{1}{{8\Pi }}\frac{{^{\partial {\text{A}}}\mu }}{{\partial {{\text{x}}_\nu }}}\frac{{^{\partial {\text{A}}}\mu }}{{\partial {{\text{x}}_\nu }}} + \frac{1}{{\text{c}}}{{\text{j}}_\mu }{{\text{A}}_\mu }} \right\}$$

(1-1)

## Keywords

Electromagnetic Field Couple System Radiate Electron Free Field Variational Procedure
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## References

- 1.P.A.M. Dirac, Proc. Roy. Soc.
*A167*, 148 (1938).ADSCrossRefGoogle Scholar - 2.F. Rohrlich, Phys. Rev. Letters
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## Copyright information

© Plenum Press, New York 1973