Single-Particle Electrodynamics - Assassination Science

6.2 Previous analyses
To the author’s knowledge, the classical radiation reaction problem for particles
carrying dipole moments has only been considered twice before: by
Bhabha and Corben [40] in 1941, using the Dirac stress-energy method of
derivation; and in a related analysis in 1989 by Barut and Unal [35], which
did not consider the problem on completely classical grounds, but instead
employed a semiclassical “zitterbewegung” model of spin.
In Section 6.2.1, we briefly review the work of Bhabha and Corben, following
by a review of the Barut–Unal analysis in Section 6.2.2.
6.2.1 The Bhabha–Corben analysis
As should by now be apparent, Bhabha and Corben attacked most of the
oustanding problems of classical particles carrying dipole moments in their
1941 paper [40]. The question of the radiation reaction is no exception.
Bhabha and Corben used the method developed by Dirac only a few years
earlier [68], of surrounding the worldline of the particle with a small tube,
and considering the mechanical energy, momentum and angular momentum
crossing this tube, for arbitrary motion of the particle. From conservation
requirements, one can then deduce the force and torque on the particle.
The method of Dirac was, at the time, a vast improvement on the Lorentz
method of derivation, as it was manifestly covariant. The resulting covariant
radiation reaction equation of motion for a charged particle is for this
reason referred to as the Lorentz–Dirac equation. However, the basic Dirac
method also has its drawbacks, alluded to in Section 6.1. In its raw form,
it requires the form and coëfficient of the inertial term to be simply guessed
at (see Dirac’s derivation [68]). This problem of arbitrariness has been overcome,
in more recent times, by considering the retarded and advanced fields
with somewhat more care [203, 204, 205]; or, somewhat more elegantly, math-
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