Single-Particle Electrodynamics - Assassination Science

quantum number” rule, as far as spin is concerned, we now finally find its
correct point of insertion into our conceptual frameworks.
An heuristic argument may be given that explicitly shows this transition
from the classical theory, to the first-quantised theory, and then to the
second-quantised theory, for the current example, which we shall now outline.
Let us return to the classical radiation reaction equation of motion for
the spin of the stationary neutron, from equation (6.146):
˙σ = σ×Ω RR , (6.160)
where
Ω RR = 2 µ 2 ...
σ. (6.161)
3 4πs
To first make the transition to the first-quantised theory, for a spin-half
particle, we need to introduce the rest-frame two-spinor
(
a
|ψ〉 ≡
b
)
(6.162)
into (6.160), in some way. From Ehrenfest’s theorem, we know that expectation
values of operators should be describable classically. Now, for the lefthand
side of this equation, we know, from our experience with the Thomas–
Bargmann–Michel–Telegdi equation, that this generalisation is simply
d t 〈ψ|σ|ψ〉 ,
namely, the time-derivative of the expectation value of the spin is the quantity
described by the classical equations. For the right-hand side of (6.160),
however, we must be more careful. Since this equation describes radiation
reaction, we in fact require the coöperation of the spin-half particle twice:
once to emit the radiation, and then once again to receive the effects of this
radiation—as with the classical derivation of this chapter; this is why there
are two factors of µ present. Now, if we are to involve the spin-half particle
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