It began with the *Feynman diagram* which I introduced
earlier in the context of relativistic kinematics.
In Fig. 1
I show the Feynman diagrams for single and double photon exchange
in *quantum electrodynamics* or ,
for which Richard P. Feynman
shared a Nobel Prize.
As before, I will draw Feynman diagrams "left to right"
instead of the conventional "down to up."
The idea of was (and is) that *all* electromagnetic
interactions between charged particles can be described in terms
of the *exchange of photons* created by one particle
and destroyed by another. The simplest case is the "first-order"
diagram in Fig. 1, where two electrons exchange
a *single* photon. The next (second-order) process is
a factor of less important, where
is the *fine structure constant*
(not a very mnemonic name any more), which is (sort of)
the *strength* of the "vertex" (the point where
the photon begins or ends). Because each successive diagram
(single photon exchange, double photon exchange, triple photon exchange
) is a factor of about 19,000 less important than the one before,
is a *perturbation theory* that *converges very rapidly*.
That is, you can get a pretty accurate result with very few diagrams.

Each diagram, you see, is *rigourously equivalent*
to a big messy integral which is definitely less appealing to
the brain's right hemisphere; but the big integral can be evaluated
to give the correct formula for the interaction of the two
electrons *to that order in*
, properly taking
into account all the ramifications of *quantum field theory*.
Which is...?
Let's take another step back
for better perspective.

Jess H. Brewer - Last modified: Mon Nov 23 14:40:36 PST 2015