Single-Particle Electrodynamics - Assassination Science

(Note that the change in metric has already been absorbed into (D.7).) The
Cohn and Wiebe U α , however, must simply be replaced by its corresponding
parts: from (D.6) we have
U µ ≡ − Rµ
ρ − V µ −→ ϕζ µ − U µ .
We can now compute a U and ȧ U : from (D.4), we have
a U ≡ (a·U) −→ ϕ( ˙U ·ζ) − ( ˙U ·U) ≡ ϕ(ζ · ˙U) ≡ ϕ ˙χ,
ȧ U ≡ (ȧ·U) −→ ϕ[Ü ·ζ] − [Ü ·U] ≡ ϕ¨χ + ˙U 2 ,
where in the last expression we have made use of the identity
(U · ˙U) = 0.
D.5 Verification of the retarded potentials
We now verify that the conversions of the expressions used by Cohn and
Wiebe for the four-potential A µ generated by the particle, equations (D.8)
and (D.9), agree with the analysis of Chapter 5.
(In Chapter 5, the potentials
were actually bypassed in favour of the physically observable field
strengths F αβ .) A by-product of this verification will be the identification of
the remaining symbols used in [54].
Firstly, Cohn and Wiebe’s electric charge potential (D.8) is notationally
converted using the translations of Section D.4:
A µ CW = eϕU µ
4π . (D.11)
Using (5.15), (5.22) and (5.19) and integrating, we obtain the equivalent Lorentz-gauge
expression for the retarded potential in the notations of Chapter 5,
A µ JPC = qϕU µ
4π . (D.12)
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