Some notes on non-abelian gauge theory

Non-Abelian Gauge Theory Lecture Notes, Based on Srednicki §24 & §69 

This is the lecture notes I used for this week's lecture of PHYS 682. We ended up to Yang-Mills Lagrangian, \[ \mathcal{L}_\text{YM} = -\frac{1}{4} F^{\mu\nu a}F_{\mu\nu}^a + \bar\psi_i \left( i \gamma_\mu D^\mu_{ij} - m \delta_{ij} \right) \psi_j \] where $D^\mu_{ij} = \partial^\mu \delta_{ij} - i g A^{\mu a} \tau^a_{ij}$ is the gauge covariant derivative; $F^{\mu\nu a} = \partial^\mu A^{\nu a} - \partial^\nu A^{\mu a} + g f^{a b c}A^{\mu b} A^{\nu c}$ is the field tensor.