Single-Particle Electrodynamics - Assassination Science

fields. These products are labelled as follows:
One finds
ϕ ≡ (ζ ·U) −1 ,
ψ ≡ (ζ ·Σ ),
˙χ ≡ (ζ · ˙U),
˙ϑ ≡ [U · ˙ Σ ],
˙ψ ≡ [ζ · ˙ Σ ],
¨χ ≡ [ζ ·Ü],
¨η ≡ [ζ · ¨Σ ].
ϕ −1 = Rγ − Rγ(v·n),
ψ = −R(σ ′·n) + ϕ −1 γ(v·σ ′ ),
˙χ = −Rγ 2 ( ˙v·n) + ϕ −1 γ 3 (v· ˙v),
˙ϑ = γ 2 ( ˙v·σ ′ ) + γ 4 (v· ˙v)(v·σ ′ ),
˙ψ = −Rγ( ˙σ ′·n) + ϕ −1 γ 2 (v· ˙σ ′ ) + ϕ −1 γ 2 ( ˙v·σ ′ ) − Rγ 3 (v·σ ′ )( ˙v·n)
+ 2ϕ −1 γ 4 (v· ˙v)(v·σ ′ ),
¨χ = ϕ −1 γ 4 ˙v 2 − Rγ 3 (¨v·n) + ϕ −1 γ 4 (v·¨v) + 4ϕ −1 γ 6 (v· ˙v) 2
− 3Rγ 5 (v· ˙v)( ˙v·n),
¨η = −Rγ 2 (¨σ ′·n) + ϕ −1 γ 3 (v· ¨σ ′ ) + 2ϕ −1 γ 3 ( ˙v· ˙σ ′ ) + ϕ −1 γ 3 (¨v·σ ′ )
+ 2ϕ −1 γ 5 ˙v 2 (v·σ ′ ) − Rγ 4 (v· ˙v)( ˙σ ′·n) − Rγ 4 (v·σ ′ )(¨v·n)
− 2Rγ 4 (v· ˙σ ′ )( ˙v·n) − 2Rγ 4 ( ˙v·σ ′ )( ˙v·n) + 5ϕ −1 γ 5 (v· ˙v)(v· ˙σ ′ )
+ 5ϕ −1 γ 5 (v· ˙v)( ˙v·σ ′ ) + 2ϕ −1 γ 5 (v·¨v)(v·σ ′ ) + 10ϕ −1 γ 7 (v· ˙v) 2 (v·σ ′ )
− 5Rγ 6 (v· ˙v)(v·σ ′ )( ˙v·n).
436