Single-Particle Electrodynamics - Assassination Science

F µν
+ 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] }
,
(−2) = − e {− 3 a U
4πmρ 2 2 ρ M [να U α R µ] + 2ρṀ[να 1 U α R µ] + 3 2 a UM [να U α U µ]
+ 1 2 M [να U α a µ] − a U M µν + ρṀ[να 1 }
R α U µ] + Ṁ µν + mV [ν U µ]
(−3) = + e {
− 3 }
4πmρ 3 2 M [να U α U µ] + M µν . (D.7)
F µν
We also rewrite the potentials (D.1) and (D.2) in terms of the converted
quantities:
A µ n.s. = + eV µ
,
(D.8)
4πR α V
( α
A µ e d M µν )
R ν
s = −
. (D.9)
8πmR α V α dτ R β V β
D.4 Conversion of notation
We now turn to the task of converting the notation of Cohn and Wiebe into
the corresponding notation used in this thesis.
The easiest conversions involve a simple change in symbol. Clearly,
,
V α −→ U α ,
R α −→ ζ α ,
a µ −→ ˙U µ ,
ȧ µ −→ [Ü µ ].
(D.10)
The quantity ρ is also easily recognised: from (D.4), we have
ρ ≡ −(R·V ) −→ −(ζ ·U) ≡ −ϕ −1 .
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