Single-Particle Electrodynamics - Assassination Science

where φ(t) ≡ Ω P t. We then find
Ω ′ RR = Ω 3 P γ 2 σ×i − 8Ω 2 MΩ P γ 4 σ×i + 2Ω 3 Mγ 3 (γ + 1) −2 σ×i
− 4Ω 3 Mγ 5 (γ + 1) −2 σ×i + 2Ω 3 Mγ 7 (γ + 1) −2 σ×i
− 3Ω M Ω 2 P γ 2 (γ + 1) −2 σ×i − 3Ω M Ω 2 P γ 3 (γ + 1) −3 σ×i
+ 6Ω M Ω 2 P γ 5 (γ + 1) −2 σ×i − 3Ω M Ω 2 P γ 6 (γ + 1) −3 σ×i
+ 2Ω 2 MΩ P γ 2 (γ + 1) −3 σ×i + 20Ω 2 MΩ P γ 5 (γ + 1) −1 σ×i
− 10Ω 2 MΩ P γ 6 (γ + 1) −2 σ×i + 2Ω 2 MΩ P γ 7 (γ + 1) −3 σ×i .
Substituting the Lorentz–Thomas result of
Ω P = (1 + aγ)Ω M ,
where
a ≡ g − 2
2
is the magnetic anomaly, we find
Ω ′ RR = −Ω 3 Mγ 3 σ×i + 2Ω 3 Mγ 5 σ×i − Ω 3 Maγ 3 σ×i + 4Ω 3 Maγ 5 σ×i
+ 3Ω 3 Ma 2 γ 5 σ×i + Ω 3 Ma 3 γ 5 σ×i .
This result is discussed in Chapter 6.
G.5 retfield: Retarded fields
G.5.1
Introduction
This program verifies that the explicit expressions obtained by the author for
the retarded fields agree with those extractable directly from the manifestlycovariant
expressions.
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