Source: Quanta Magazine, Jul 2016
Feynman diagrams look to be pictures of processes that happen in space and time, and in a sense they are, but they should not be interpreted too literally. What they show are not rigid geometric trajectories, but more flexible, “topological” constructions, reflecting quantum uncertainty. In other words, you can be quite sloppy about the shape and configuration of the lines and squiggles, as long as you get the connections right.
Feynman found that he could attach a simple mathematical formula to each diagram. The formula expresses the likelihood of the process the diagram depicts. He found that in simple cases he got the same answers that people had obtained much more laboriously using fields when they let froth interact with froth.
Feynman diagrams remain a treasured asset in physics, because they often provide good approximations to reality. Plus, they’re easy (and fun) to work with. They help us bring our powers of visual imagination to bear on worlds we can’t actually see.
The Feynman diagram representation of a process is most useful when a few relatively simple diagrams supply most of the answer. That is the regime physicists call “weak coupling,” where each additional complicating line is relatively rare. That is almost always the case for photons in quantum electrodynamics (QED), the application Feynman originally had in mind. QED covers most of atomic physics, chemistry and materials science, so it’s an amazing achievement to capture its essence in a few squiggles.
with modern computers we can go back to the truly fundamental field equations and calculate fluctuations in the quark and gluon fields directly. This approach gives beautiful pictures of another kind: