a Feynman diagram

A Feynman diagram is the back-of-the-envelope sketch that turned the fearsome bookkeeping of quantum field theory into something you can doodle. Draw a couple of lines coming in, a vertex where they meet, a wiggly line for an exchanged photon, and lines going out, and you have captured, in a cartoon, one contribution to the probability that particles will scatter. Richard Feynman's pictures are so intuitive that it is easy to forget they are not pictures at all, but a precise mnemonic for writing down a specific mathematical integral.

Formally, a Feynman diagram represents one term in the perturbative expansion of a scattering amplitude. External lines are the incoming and outgoing real particles; internal lines are propagators representing virtual particles that are not directly observed and need not obey the usual energy-momentum relation; and each vertex encodes an interaction whose strength is a power of the coupling constant. The Feynman rules translate each element, line and vertex, into a factor, and multiplying them and integrating over the undetermined internal momenta gives the amplitude for that process. The full amplitude is the sum over all diagrams, ordered by the number of vertices (tree diagrams, then one-loop, then two-loop, and so on).

The power of the method is that in a weakly coupled theory like QED the higher-order diagrams contribute less and less, so a handful of diagrams already gives spectacular accuracy. The danger is taking the cartoon literally. An internal line is not the path of a real particle flitting through space, and a diagram with the electron 'emitting then reabsorbing' a photon is not a movie of events in time; it is one term in a sum of amplitudes that must be added coherently, including their quantum interference. In strongly coupled QCD at low energy the series does not converge usefully at all, and diagrams give way to lattice simulation.