Single-Particle Electrodynamics - Assassination Science

which can be seen to encompass all of the results of the preceding sections.
As has been noted earlier, the correct procedure when taking the propertime
derivative
d τ (Σ ·F )
or
d τ (Σ · ˜F )
in (4.70) is to use the product rule on the components Σ α , F µν and ˜F µν ; the
former thus yields the partial derivative [ ˙ Σ ] appearing in (4.71), and the
latter two yield the convective derivatives
(U ·∂)F
and
(U ·∂) ˜F .
The published paper [65] of Appendix F unfortunately uses instead the covariant
derivative ( ˙ Σ ); again, as has been noted in previous sections, this
incorrect procedure removes the redshift force, which the author now realises
should be present.
Due to the fact that the author only obtained the redshift force shortly
before this thesis was printed, a re-analysis of the uncoupled equations of
motion, à la that presented in Appendix F, has not yet been performed.
However, we intend to perform such an analysis in the near future.
4.4 What does the Dirac equation say?
Throughout this chapter, we have considered the dipole equations of motion
purely from the point of view of classical physics. But, as noted in
the Abstract of this thesis, the Dirac equation also belongs to the field of
single-particle electrodynamics: it considers only a single particle, and the
electromagnetic field is treated as a classical field. From Ehrenfest’s theorem,
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