Relativity – Week 05
During this week we finished the discussion of action principles and started Yang-Mills theory.
We looked at conservation of charges and currents. We also considered some gauges. Then we turned to pair creation and annihilation. On Wednesday we started with Yang-Mills theory as a non-abelian generalization of electromagnetism. Today we covered some formalities of Yang-Mills theory, like covariant derivatives, Lie group elements, gauge fields and the field strengths. We also saw how to generalized actions with abelian gauge fields to Yang-Mills fields with the general prescription of changing partial derivatives for covariant derivatives. It is very interesting that the action for the Yang-Mills field itself is written in a very similar way to the action of the electromagnetic field, with an additional term that comes from the noncommutativity. This term introduces interactions of the Yang-Mills field with itself.
More information can be found in sections IIIB2-5, IIIC1 of Fields.
Update: I have noticed that reading section IB2 might be useful to follow some of the notation. (Besides thee obvious fact that the author keeps referring to this section through the discussion of Yang-Mills theory…)