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.

**Figure:**
**Feynman diagrams** for electromagnetic electron-electron
scattering in first order (left) and second order (right).

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.