In simple terms, what is the Yang–Mills theory, and why is it important?



In simple terms, what is the Yang–Mills theory, and why is it important?

In: Physics

The Yang-Mills theory is used to understand elementary particles, electro-magnetic forces, and chromodynamics (theory of strong forces). Using Yang-Mills to understand the little stuff, helps us understand the big stuff/”Standard Model” of physics.

(This was hyper simplified, making it sound a bit wrong.)

So, let’s begin with what’s meant by “a theory”. For ELI5 purposes, it means writing down a bunch of particles, forces, masses, interactions, and interaction strengths. Physicists call it a Lagrangian density – but it’s basically just a list of stuff and the rules for stuff.

Now, you can write down any Lagrangian density, and it’ll be *a* theory – this is easy, literally anyone can do it. But not all theories are going to “work”. One way they can be wrong is that they can be missing particles, or missing forces, or missing interactions. But another problem the can have is they can fail to be Renormalizable.

The ELI5 for renormalizability is: when you go to make a prediction for non-renormalizable theory, you get infinity. That’s bad. We don’t want that. When you do it for a Renormalizable theory, you get an actual prediction. Which is good. We can test it, see if this theory is consistent with experiment.

And here’s why Yang-Mills theories are important:

All Yang-Mills theories are Renormalizable.

This was proven by some Dutch fellows who received Nobel prizes in physics for it (and proceeded to argue about who deserved credit) a few decades ago.

To be fair, Yang-Mills theories have some other properties that make them attractive, but the main importance is that, when you make a theory, if it’s YM, then you can know it’s Renormalizable and you can make predictions with it.