Single-Particle Electrodynamics - Assassination Science

B.2.2
The field strength tensor
The six-vector F (x) is referred to as the electromagnetic field strength tensor,
and is obtained from A(x) by means of the definition
F ≡ ∂∧A.
(B.1)
B.2.3
The homogeneous Maxwell equations
From the definition (B.1), one immediately finds the homogeneous Maxwell
equations,
∂ α F βγ + ∂ β F γα + ∂ γ F αβ ≡ 0.
(B.2)
Note that magnetic charges (“monopoles”) cannot exist if the four-potential
A(x) is assumed to be fundamental.
B.2.4
The dual field strength tensor
The dual electromagnetic field strength tensor, ˜F (x), is obtained from F (x)
according to
˜F ≡ − 1 ×
F ,
(B.3)
2
where in (B.3) we employ the four-cross-product notation defined in Section
A.8.10. From (B.3), one can show that the reverse transformation is
F ≡ 1 2
טF .
(B.4)
B.2.5
The electromagnetic duality transformation
The minus sign in (B.3) might seem misplaced to some readers. It can be
traced back to the sign convention chosen for the alternating function in
Section A.5.4. The sign of (B.3) has, in fact, been chosen so that the explicit
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