I would actually beg to differ, on that one: Feynamn diagrams are a big part of QED, and you could probably train most nine year olds to construct valid Feynamn diagrams (though I can’t promise that the kid would know what to do with them, of course).

To further explain: The goal in any theory of particle physics is to be able to calculate two sorts of numbers: Cross sections and lifespans. A cross section is a measure of the likelyhood of two particles interacting to produce some particular collection of output particles (which might or might not be the same as your original particles). It’s measured in area units, and can rougly be thought of as the size of your target for your particle accelerator. A lifetime is the average amount of time a particular particle will last, before decaying into other particles (this can be infinite, for some particles).

It turns out that both of these quantites are related to a quantity called the amplitude, which describes the process. Feynman found that one could calculate amplitudes with the aid of simple diagrams, constructed according to a simple set of rules. For QED, the diagrams consist of squiggly lines, representing photons, lines with arrows on them, representing electrons/positrons, and vertices where the lines meet, consisting of one arrow-line coming in at the vertex, one arrow-line going out, and one squiggly line.

For instance, suppose we’re interested in the cross-section for a photon scattering off of an electron. That is, we have a process where one photon and one electron go in, and one photon and one electron come out. At the bottom of the page (representing the time before the interaction), we have a squiggly line heading towards the middle of the page for the photon coming in, and an arrow-line pointing up representing the electron (if it were a positron, the arrow-line would point down). At the top of the page, we also have a squiggly line coming out, and an arrow-line pointing up coming out, since at the end of this particular process we still have a photon and an electron. Now, in the middle of the page, we want to make some combination of lines connected together with those vertices, such that we connect all of the lines at the top and bottom of the page. For instance, we might connect our two incoming lines at a vertex, with the third leg of the vertex being another arrow-line all by itself pointing up, and then attach another vertex to that arrow-line that turns into the arrow-line and the squiggly line at the top. Once we’ve connected everything, we have a Feynman diagram for that process.

Now, for that Feynman diagram, there’s a set of rules we can use, based on the number of vertices we have, the number of lines, and how the vertices are connected, to determine an amplitude for that particular Feynman diagram. If we draw all of the Feynman diagrams for a given process, and add up all of the amplitudes for them, we get the total amplitude for the process, and from that we can calculate the cross section or the lifespan.

The problem with this is that, for any given process, there are an infinite number of valid Feynman diagrams you can draw. Fortunately, though, in QED and electroweak theory, the amplitude of a diagram decreases as the diagram gets more complicated (more vertices), so if you only draw the simple diagrams, you can get a good estimate of the true amplitude (the more complicated diagrams you draw, the better the estimate). In QCD, the theory of the strong force, however, this doesn’t usually work: For most QCD processes, the amplitude increases as the diagrams get more complicated, and there’s no limit to how complicated a diagram can get, so you can’t do the sum.

Asymptotic freedom refers to the fact that, for very high particle energies, QCD diagrams do get weaker as they get more complicated. So if and only if your particles are high enough energy, you can use Feynman diagrams to determine cross sections in QCD.