This post will be broken down into three parts: first, a few basics about commutators (for everyday use in physics), then the solutions to Problem Sheet 3, and finally an attempt at explaining the physical meaning of commutators (if you’re not a PHY251 student you might want to jump straight to that).
Last week I introduced the basics of EFT from the perspective of renormalization; today, I’m considering a practical example: getting an EFT for QCD without the top quark, that is, trying to simplify QCD at energy scales .
I’ve started learning effective field theory (EFT)
Last week I talked about SSB and focused on its physical interpretation and effects, looking at fields and potentials while avoiding (as much as possible) to mention group theory. This is why I’ve decided to make the following into a separate post, where I’ll briefly re-emphasize a point I’ve already made in the last post (how we count massless modes in the broken theory) from a group-theoretic perspective.
Here I give a brief overview of spontaneous symmetry breaking (SSB) in the way I would present it to experimental particle physicists, assuming only little QFT background and barely even mentioning group theory. We will start with one-dimensional discrete symmetry breaking, extend it to continuous SB, mention Goldstone’s theorem and introduce the Higgs mechanism, before jumping to electroweak theory and obtaining the main result of interest: the generation of masses for the and gauge bosons in the Standard Model.
Here I’m assuming some prior knowledge of QFT and the basics of differential geometry, and I will try from those basics to motivate the construction of the well-known Yang-Mills gauge Lagrangian
The following are the (incomplete, possibly erroneous) notes I took during Thomas Sotiriou’s talk at the YETI 2017 conference in Durham.