In the covariant quantization approach: (a) Prove Eq. (6.4.148); i.e., the addition of (-frac{1}{2 xi}left(partial_{mu} A^{mu} ight)^{2})

In the covariant quantization approach:

(a) Prove Eq. (6.4.148); i.e., the addition of \(-\frac{1}{2 \xi}\left(\partial_{\mu} A^{\mu}\right)^{2}\) to the Maxwell langrangian gives the equations of motion \(\square A^{u}-\left(1-\frac{1}{\xi}\right) \partial^{u}\left(\partial_{\mu} A^{\mu}\right)=0\).

(b) Complete the details of the sketch proof and show how to obtain the covariant canonical commutation relations for \(\hat{A}^{\mu}\) and \(\dot{\hat{A}}^{\mu}\) in Eq. (6.4.152).