Single-Particle Electrodynamics - Assassination Science

G µ ≡ G 1 k/k µ + G 2 k/B µ + G 3 B/k µ + G 4 B/B µ ,
H µ ≡ (H 1 γ µ + H 2 k µ + H 3 B µ + H 4 σ µν k ν + H 5 σ µν B ν ) γ 5 ,
K µ ≡ (K 1 k/k µ + K 2 k/B µ + K 3 B/k µ + K 4 B/B µ ) γ 5 ,
and where Lorentz covariance means that the coefficients F i , G i , H i and K i
can only be functions of k 2 ≡ (k·k). We are here using the definitions
{γ µ , γ ν } ≡ g µν ,
σ µν ≡ i 2 [γµ , γ ν ] ,
γ 5 ≡ γ 5 ≡ i 4! ε λµνπγ λ γ µ γ ν γ π ,
x/ ≡ γ µ x µ ,
where [x, y] denotes the commutator of x and y and {x, y} their anticommutator,
and in this section we are using units in which ¯h = 1. With the
particle on mass shell in the initial and final states, we have
(B·k) ≡ b 2 2 − b 2 1 = m 2 − m 2 = 0;
(E.2)
using also the Gordon identities,
u 2 γ µ u 1 = 1
2m u 2 (B µ + iσ µν k ν ) u 1 ,
u 2 γ µ γ 5 u 1 = 1
2m u 2 (k µ + iσ µν B ν ) γ 5 u 1 ,
u 2 iσ µν B ν u 1 = u 2 k µ u 1 ,
u 2 B µ γ 5 u 1 = u 2 iσ µν k ν γ 5 u 1 ,
we can reduce the number of independent terms in (E.1). In particular, we
may remove (say) the terms F 3 , F 5 , H 3 and H 5 as redundant; all of the terms
G i and K i lead to terms that are either excluded by Lorentz covariance, are
included in other terms, or vanish by (E.2), or by virtue of the fact that
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