Single-Particle Electrodynamics - Assassination Science

and the Kolsrud–Leer [124] retarded potential for a particle carrying electric
and magnetic dipole moments (or “spin” potential),
A µ s =
e
2mR α V α
(
d M µν )
R ν
. (D.2)
dτ R β V β
(Kolsrud and Leer [124] did not include the factor e/2m in their expression;
also, Cohn and Wiebe have switched the order of the product of R ν and
M µν , effectively introducing an extra minus sign.) It should be noted that
this expression, (D.2), differs considerably from that obtained in 1969 by
Cohn [53]; the latter result is wrong, as pointed out by Kolsrud [125], and
admitted by Cohn and Wiebe in the paper we are currently considering [54].
Cohn and Wiebe explicitly note that they are using a (+, +, +, −) metric,
world length dτ 2 = −g αβ dX α dX β , where X α denotes a field event (i.e., an
arbitrary four-position in space). Z α is used for the particle event (at the
retarded time), V µ = dZ µ /dτ (this is misprinted as dX µ /dτ in the paper),
and R α = X α − Z α . The tensor M µν is simply listed as “the moment
tensor characterising the particle”; we shall return to the question of its
normalisation value shortly.
For the remaining expressions, the particle is assumed to have no electric
dipole moment (in its rest frame), so that M αβ V β = 0. After some
manipulations, they find that
where
F µν
F µν = F µν
(−1) + F µν
(−2) + F µν
(−3) ,
(−1) ≡ − e { 3
mρ 2 2 a2 UM [να U α R µ] + 1 2 aUṀ[να U α R µ] + a U
ρ Ṁ [να R α R µ]
+ 1 2ȧUM [να U α R µ] − 1 2 a2 M [να U α R µ] − 1 2 a UM [να a α R µ]
+ 1
2ρ ¨M [να R α R µ] + ma [ν R µ] + ma U V [ν R µ] }
,
379