Single-Particle Electrodynamics - Assassination Science

where in (5.44) we have noted that B q 2 (and hence B ′q
2 ) satisfies both (5.34)
and (5.35).
Equations (5.41), (5.42), (5.43) and (5.44) are the final, simplified expressions
for the retarded fields generated by a point electric charge, in the
author’s notational system.
5.4 The retarded dipole fields
In this section, we compute the retarded electromagnetic fields generated by
an arbitrarily moving particle possessing magnetic and electric dipole moments,
in addition to electric charge.
It will be found convenient to assume from the outset that the dipole
moments are fixed in magnitude, such as is true for the intrinsic moments
of spin-half particles. We may then employ the unit spin four-vector Σ α of
Section G.4.4 to denote the direction of the dipole moment from the outset,
with a constant numerical coëfficients d and µ. However, it should be noted
that the angular momentum connotation of Σ is not used at all, in the
considerations of this chapter. In other words, the results are completely
applicable to classical dipoles in which the (fixed) dipole moment vector and
the spin angular momentum vector have no definite relationship; one should,
in these cases, simply replace σ, in the results of this chapter, by d or µ as
appropriate.
5.4.1 The field Lagrangian
Our first step is to return to the classical free-field Lagrangian density of the
electromagnetic field, equation (5.1):
L free = 1 4 F αβ F αβ .
To this Lagrangian density we must add terms corresponding to the interaction
between the electromagnetic field and the electric and magnetic dipole
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