1. From $U(y,x)\to e^{i\alpha(y)}U(y,x)e^{-i\alpha(x)}$ and $n\cdot D\psi=\lim_{\epsilon\to 0}\frac{\psi(x+\epsilon n)-U(x+\epsilon n,x)\psi(x)}{\epsilon}$, find the transformation laws of $A_\mu$, and the formula for $D_\mu$ as a function of $A_\mu$ if $U(x+\epsilon n,x)=1-i\epsilon n\cdot A$.
2. Write the QCD lagrangian as a function of the coloured fields $A_\mu^a$, starting from its expression as a function of the fields $\mathbb A_\mu$ and using ${\mathbb A}_\mu=\sum_{a=1}^8 \frac{\lambda_a}{2} A_\mu^a$.
3. Derive the equation of motion of the field $A_\mu^a$.