Feynman argument?

Can anyone point me to some background for what looks like a bit of
sleight-of-hand in Feynman's half of the 1968 Dirac Lectures
(published together with Weinberg's lecture, in "Elementary Particles
and the Laws of Physics", Cambridge UP, 1987).

Feynman explains the existence and nature of antiparticles in a
remarkably intuitive way on p. 10, but the argument rests on something
leading to a point that seems far from intuitive (that an amplitude
"cannot be zero outside the light cone..."), on p. 8, and I would
greatly appreciate a relatively elementary reference that would enable
me to work through the necessary background:

"If a function f(t) can be Fourier decomposed into positive
frequencies only, i.e. if it can be written

f(t) = [Integral from 0 to Inf.] exp[-iwt] F(w) dw

then f cannot be zero for any finite range of t, unless trivially it
is zero everywhere.
[OP: sounds reasonable]
The validity of this theorem depends on F(w) satisfying certain
properties, the details of which I would prefer to avoid.
[OP: that's the sleight-of-hand; move on half a page]
....The theorem applies directly.
[OP: to an amplitude defined a few pages earlier]
In particular it cannot be zero outside the light cone of X1
[OP: Huh??? ].
In other words, there is an amplitude for particles to travel faster
than light and no arrangement of superposition (with only positive
energies) can get around that."

In essence, as I read it, Feynman's saying that a particle seen from
one reference frame can appear as an antiparticle from some others.
Wonderful!

But how does the amplitude "leak out of" the light cone? It sounds
like a sort of relativistic tunneling, which seems counterintuitive?

Can anyone suggest a reference that provides the background to this,
please?.

Pellis

.

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