Recent content by chrispb

In YM, the three point vertex coefficient and the four point coefficient are related to each other; one goes like g p_mu, and the other is g^2. The second is necessary to have a gauge-invariant Lagrangian. What's neat about YM is that given the three-point vertex at tree level, one can use it to...

I'm not really sure what you mean; sure, you can associate SU(2) with unit quaternions and U(1) with unit complex numbers, but you can't associate any group structure to unit octonions because they're not even associative. They do have an automorphism group of G2, but that's about as close to...

By itself, no, but if you tell me that the SU(2) x U(1) is broken to a U(1) subgroup (as it is in our universe), then that tells you that there must be something serving as a higgs field doing the breaking. However, it doesn't tell you that that Higgs field is elementary. Also, note that when...

The list of particles is probably not complete; there are likely new states associated with quantum gravity. The set of particles is certainly not unique. I can add a fourth generation without spoiling any symmetries; it's just that we haven't seen any such thing yet.

I would also expect it to be zero; I would expect that you'd find wavefunction renormalization that respects supersymmetry, provided you have no explicit SUSY-breaking terms in your Lagrangian in the first place. Have you verified your calculation?

People say that such terms are "pure counterterm", meaning adding a local counterterm of the form delta m^2*phi^2 term in your action is sufficient to cancel such divergences; there's no leftover bit that depends on p or mu, the renormalization scale.

I didn't read carefully enough to spot where you made the mistake, but I'll tell you the answer; the Klein-Gordan operator acting on a plane wave returns m^2 times the plane wave, even in the relativistic limit. Therefore, no matter what order you do things, you should expect a cancellation...

U(1) symmetries can indeed be anomalous.

More group-theoretically, a little group is the group that leaves some particular state invariant. Poincare transformations act on good old quantum mechanical states; the little group of the state of one massive particle in its rest frame is therefore the SO(3) of rotations around it.

I learned most of my group theory from Dresselhaus and Tinkham's Group Theory books, Georgi's Lie Algebras in Particle Physics (available online for free, though not as related to this issue in particular) and Fecko's Differential Geometry and Lie Groups for Physicists. I especially like the...

The mechanism by which the higgs gives other particles mass is related to the reason it has a mass itself. However, the higgs having a mass alone is insufficient to generate masses for other particles; the more crucial feature is that it develops a vacuum expectation value (a vev), meaning that...

U(2) = SU(2) x U(1), maybe mod Z2. It's been a little while. You have the U(1)_L and U(1)_R. Then you define U(1)_V = U(1)_L + U(1)_R and U(1)_A = U(1)_L - U(1)_R.

@tom.stoer: A vertex of the form gluon-photon-quark is excluded by symmetry arguments. I'm assuming one would get this external gluon as ISR or FSR off a pp collision or something of the sort; the initial state was a color singlet, so the final state had better be one too. The gluon will indeed...

126bar is the complex conjugate of the 126 representation.

1) Particles can only decay to 2+ body states with less mass than them. Since gluons are massless, it follows that they are stable. 2) Pure gluons don't exist; QCD is confining, so a single gluon will hadronize into color singlets. 3) The photon doesn't carry color charge, so it doesn't...