This week saw the end of Yang-Mills theory and the beginning of gravitation. We started gravity by considering the case when the metric is just a scalar function of the spacetime coordinates times the Minkowski metric. This has the form of conformal transformations.
It has been very hectic during the last few weeks here in Stony Brook. I do not want to fail on my goal to summarize my classes every week, so now that I have found some free time I am going to catch up. So from now until midnight I will try to catch up on all those weeks that I have not wrote about.
Not like anybody care.
Sorry, sorry and sorry for not posting in weeks. It is sad that there does not seem any time to catch up in the future. A quick summary of what we done so far on my classes:
We finished the discussion of Yang-Mills theory and then started considering the gauge group for the general coordinate transformations. In turns out that in order to incorporate fermions (spinors) one needs to introduce a local Lorentz transformations. Most of last week was going through Siegel’s notation and writing out the usual identities and expressions for covariant derivatives, torsion and curvature tensors and vierbeins. Yesterday we discussed some gauge choices and some conditions to deal with redundant degrees of freedom (i.e. setting the torsion equal to zero).
We finally finished with finite group theory and started with Lie groups and algebra. In class we saw how SU(2) is the covering group of SO(3) and we also considered the covering group of the Lorentz group. We listed the classical algebras and hopefully today we will classify all Lie algebras and mention the exceptional algebras.
Quantum field theory
Physics is finally creeping back to quantum field theory. We constructed states that have particle interpretations and basically solved the free theory. Today we discussed Green functions for the Klein-Gordon equation. Next Thursday we should treat interacting fields and soon we will start with path integrals.
During this week we finished the discussion of action principles and started Yang-Mills theory.
During this week we studied the Poincaré group and we started with the quantization of scalar fields.
Things are getting pretty busy here in Stony Brook. Maybe the time spacing of my weekly post is going to increase a bit. Still have last week’s worth of group theory to write about, including the Dirac matrices in dimensions 2 through 11.