Single-Particle Electrodynamics - Assassination Science

In Einsteinian mechanics, the electromagnetic field satisfies Maxwell’s
equations:
∇·B ≡ 0, (2.8)
∇×E + ∂ t B ≡ 0, (2.9)
∇·E ≡ ρ, (2.10)
∇×B − ∂ t E ≡ J. (2.11)
The homogeneous Maxwell equations (2.8) and (2.9) tell one that the six
components of the fields E and B may in fact be completely specified in
terms of four quantities A µ ≡ (ϕ, A):
E ≡ −∇φ − ∂ t A,
B ≡ ∇×A. (2.12)
However, the A µ are not directly manifested physically. They are also arbitrary
up to a gauge transformation:
A µ −→ A µ + ∂ µ Λ.
The electromagnetic field also possesses mechanical energy, mechanical
momentum and mechanical angular momentum densities. These are given
by
W ρ (x) =
2{ 1 E 2 (x) + B 2 (x) } , (2.13)
p ρ (x) = E(x)×B(x), (2.14)
s ρ (x) = x×p ρ (x). (2.15)
The former two densities are a part of the electromagnetic mechanical stressenergy
tensor, T µν :
T 00 =
2{ 1 E 2 + B 2} ,
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