Single-Particle Electrodynamics - Assassination Science

the position operator x yields
md t x = b − qA − g − 1 µ×E + O(1/m)
g
≡ p naive ; (4.78)
and, in turn, for this operator p naive ,
F naive ≡ d t p naive
= qE + g − 1
g
{(µ·∇)B − ˙µ×E + µ×J ext
}
+ 1 ∇(µ·B) + O(1/m). (4.79)
g
These results, (4.78) and (4.79), have been collected together and cleaned up
somewhat by the author, based on the expressions found by previous workers
[88, 108, 26, 11]; but the author has not changed their mathematical content
in any respect.
4.4.3 Intepretation of the equations of motion
We now turn to the question of interpreting the equations of motion (4.78)
and (4.79), and indeed the Hamiltonian (4.77). This question has been considered,
over the years, by a number of workers; the author has, for example,
found the discussions of Barone [26] and Anandan [11, 12, 14] most helpful;
the following conclusions are in large part due to those authors.
The most puzzling aspect of the results (4.77), (4.78) and (4.79), even at
first sight, is the recurring presence of the factor
g − 1
.
g
Let us first obtain a clear understanding of what this factor represents. In
the case of a “pure Dirac” moment, i.e., an electric charge only in the Dirac–Pauli
representation, we have g = 2, and hence
g − 1
= 1 g ∣ Dirac only
2 .
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