Single-Particle Electrodynamics - Assassination Science

force is not only more powerful than the method of considering the mechanical
stress-energy tensor of the field (perfected, in the fully relativistic case,
by Dirac [68])—the latter requiring reasonable but underivable assumptions
to be made, and arbitrary constants to be fitted; the Lorentz method is also
intuitively simple to understand. The relativistic shortcomings of Lorentz’s
original derivation are simply repaired, using the formalism of Chapter 3;
one is then left with a complete, rigorous, intuitive and æsthetically pleasing
method of derivation of the radiation reaction equations of motion.
It is this method that we shall use, in this final chapter, to derive the
classical radiation reaction equations of motion for point particles carrying
electric charge and electric and magnetic dipole moments. In Section 6.2, we
review the work of Bhabha and Corben, who considered this problem in 1941,
using the Dirac stress-energy method; and a related analysis undertaken recently
by Barut and Unal, using not the classical spin formalism of this thesis,
but rather a semiclassical “zitterbewegung” model of spin. We then attack
the problem anew, beginning, in Section 6.3, with a consideration of various
aspects of the use of an infinitesimal rigid body. In Section 6.4 we introduce
the sum and difference constituent position variables, and show that their
use is not a trivial as one might naïvely expect. We then compute, in Section
6.5, the retarded kinematical quantities of the constituents of the body,
and use these results to obtain the retarded self-field expressions. The threedivergences
of these expressions are computed in Section 6.6, as the final step
of the computation of the relativistic worldline fields considered in Chapter 5.
Some necessary subtleties involved with the integration of terms in the analysis
of an inverse-cube dependence are discussed in Section 6.7. In Section 6.8
we compute the radiation reaction equations of motion themselves; these are
discussed in Section 6.9. Finally, in Section 6.10, we apply one of the equations
obtained to the Sokolov–Ternov and Ternov–Bagrov–Khapaev effects,
and highlight both the successes and limitations of the completely classical
analysis.
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