Images in space and time: Feynman diagrams

So far in this series, we’ve introduced the standard model of particle physics: we’ve made a list of the fundamental particles that make up everyday matter (plus a few extras), called fermions, and the particles that bind them together as forces (plus the Higgs particle), called bosons. All of that can be summarised in a diagram suspiciously similar to the periodic table:


This week, I’ll talk about describing collisions and interactions between these particles. This is almost universally done by using a system of diagrams invented by and named after Richard Feynman. These Feynman diagrams absorb all the calculus and group theory and complicated mathematical notation into pictures, making their interpretation quite accessible (although calculating the rules for Feynman diagrams is another story). For example, this is a photon, labelled as γ:


Once we introduce axes and directions to the diagrams, we can talk about what the photon is doing, but for now, that’s a photon. This is a gluon:


And this is a Higgs boson:


Fermions are all represented by straight, solid lines, so the labels become especially important. These particles also come with arrows — if the arrow goes backwards, we’re dealing with antimatter, not ordinary matter! (We’ll go into that a little more next week.) For the moment we haven’t specified forward and backward, but I’ll make the arrows consistent with the notation we’ll adopt by the end of the article. Here are a quark and an electron:



We could go on and draw all the particles of the standard model, but for this project we’ll stop here, since we only need four: the quark, the electron, the photon and the gluon. There’s one more thing we can do with them before we start thinking about axes and directions. Two weeks ago we said protons and neutrons must be made of quarks because of all the threes. So we can put three quarks together to represent a proton:


Of course, three quarks could also be a neutron, so labels matter. (Unless things are crystal clear from context, in which case the labels are sometimes left out.)

To go much further, we need to introduce the axes of Feynman diagrams. Bearing in mind that we’re generally trying to describe collisions between particles, we use one axis to describe the separation between the relevant particles. In fact this is the only information about position that the diagrams explicitly include. So far, two colliding particles would look like this:


Clearly the ability to represent the separation at different times is crucial. We use the diagram’s other axis to represent passing time. Then we can represent two electrons interacting by exchanging a photon like this:


Sometimes it’s easier to represent the maths behind the Feynman diagrams by starting with early times on the right and flowing towards later times on the left:


Although the left-to-right notation is more common, for all the reasons you’d expect, I’m going to need specialised Feynman diagrams that assume the right-to-left convention later, so I’ll draw time progressing from right to left from the start. Here’s a photon undergoing a process called pair production in which it turns into an electron and an anti-electron (called a positron):


And here’s a real live working diagram of a collision between an electron and a proton, mediated by a photon:


This one’s pulled directly from my thesis, so it may need a little more explanation. Since I’ve told you that the quarks make up a proton, you should be able to figure out that they’re quarks, not antiquarks and put the arrows on for yourself. The photon is labelled as γ* because it’s a “virtual particle” — we can’t measure it, since it disappears before the collision is over. This allows it to have some unusual properties that wouldn’t make sense otherwise. The blob between the photon and the quark represents the fact that while they could interact directly, we also want to consider more complicated processes. For instance, the photon could produce an electron and a positron (like in the earlier diagram) and that electron could produce another photon, which interacts with the quark. Since we haven’t specified exactly what the interaction is, we don’t know exactly what comes out the other end, so there are just a bunch of lines collectively labelled “X”. This process is called Deep Inelastic Scattering (DIS) and it’s the context for most of the work done in my MSc project (although my work is based on a slightly different diagram that also falls under the DIS heading).

That’s Feynman diagrams! Next week we’ll talk about the Feynman rules, which tell us which diagrams make sense and which don’t. Along the way we’ll also talk more about matter, antimatter and virtual particles.

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