Particle physics

As an undergraduate, my education was heavily influenced by particle physicists. They taught my classes, I did research with them, they were my mentors and heroes. In the end, I decided that particle physics wasn't for me, but I still think about it from time to time.

This year, I finally got around to taking a class in quantum field theory -- the subject that lies at the heart of particle physics. Between reading Peskin and Schroeder, sitting in class, and talking to the lecturer, I am starting to get a clearer picture of what is going on.

I'll just list a few of the interesting things I've learned so far.

1) People often say that quantum chromodynamics (QCD) is a beautiful theory because it only has one adjustable parameter (the strength of the coupling between quarks and gluons). This is because QCD is a non-Abelian gauge theory. Once you add in the fact that QCD obeys SU(3) symmetry and that dimensions of the operators have to have be less than some critical number for the theory to be renormalizable, the QCD Lagrangian is almost completely constrained. However, the constraint that the theory must be renormalizable is debatable. There could be some terms in the Lagrangian which are not renormalizable but are extremely weak in our low-energy observation range.

2) If you read any introductory book on particle physics, the first thing that is mentioned is that lepton and baryon number are conserved. That is why when a neutron decays to a proton and electron, it must also produce an electron neutrino. A muon or tau neutrino is not allowed. It turns out that this conservation might be approximate. The physics we know about (the Standard Model) only has Lagrangians which conserve these numbers. In addition, the dimension of the coupling constants are less than four (I think) which implies that we know about these interactions because they are important at low energies. But there could be other terms in the Lagrangian which only kick in at high energy beyond our current observation range. And these terms might not conserve lepton and baryon number.

3) According to the lecturer of my class, proton decay is a very strong constraint on grand unification theories (GUT). [In most GUTs, at very high energies, protons can couple to other interactions which make them decay.] The fact that the proton lifetime is experimentally limited to being greater than 10^33 years makes these theories unlikely. Of course that is his opinion. He also thought that the non-unification of quark energies was also a strong indicator that GUTs are implausible. I asked him whether future experiments might clear up the mystery. He thought that the Large Hadron Collider at CERN would be able to see something but not with great precision. The Next Linear Collider (an experiment being planned) has the technological power to do precision measurements, but currently no country wants to fund it. All-in-all, a rather depressing outlook!

My conclusion so far is that particle physics is a fascinating subject, but until there are experiments at higher energies, it is impossible to say anything coherent about speculative theories like GUTs. Of course, bona fide particle physicists say the same thing, but I'm just now starting to realize why.

I realize that this post will not make sense to 99.99% of the population. A few months ago, I wouldn't have understood it earlier. I would say that to really understand particle physics at any meaningful depth, it's imperative to take a field theory course.