Advanced quantum field theory, Lecture 11

This summer semester (2017) I am giving a course on advanced quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics, statistical physics, and quantum field theory (for a good foundation see my videos on advanced QM and QFT). The main objective is discuss the building blocks of the standard model, including, Yang-Mills theory and symmetry breaking.

Here in Lecture 11 I discuss classical nonabelian gauge theory.

[xiangsun]

Dear Prof. Osborne
Thanks very much for uploading this great lecture.
However I get lost at 18:17 and 20:42
1.What are these two independent fields and what's the motivation of introduction of them.
2.Why the composite field is 8 by 1? Is it because \psi_{1} (\psi_{2}) is relatistic dirac field described by 4 by 1? If so, in previous contents, when saying SU(2) is 2 by 2 matrix, is it to say it mixes the two subspaces representing the two independent fields, than components of \psi_{1} (\psi_{2}) ?
Sincerely,
Xiang

[jungyunhan]

Dear Prof. Osborne,

Thank you for very nice lecture on non-abelian gauge theory! I am learning a lot from this lecture.

I have a one very simple question on the construction of the SU(2) gauge matrix A.

I understand why do we need 3 Pauli matrices as they are basis set of su(2) algebra.

But what about 2 by 2 identity matrix? Is there any reason to exclude this? I guess that identity part is simply reduced to U(1) gauge theory again?

Thank you very much in advance.

Sincerely,

JungYun.

[simonb.]

I think more details in the presented calculations would work miracles. I know its all about time-efficiency, but this is starting to get unclear :)