Classical electromagnetism (with no sources) follows from the actions$$S = \int d^4x\left(-{1\over4}F_{\mu\nu}F^{\mu\nu}\right),\text{ where }F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu.$$The Lagrangian for $A_\mu$, including a gauge fixing term, is$$\mathcal{L} = -{1\over4}F^2 - {\lambda\over2}(\partial_\mu A^\mu)^2.$$Could anyone show or supply me a reference for the computation of the equal time commutators $[\dot{A}_\mu(\textbf{x}), A_\nu(\textbf{y})]$ and $[\dot{A}_\mu(\textbf{x}), \dot{A}_\nu(\textbf{y})]$ for general $\lambda$ and the fact that they simplify for $\lambda = 1$? I need this result, but I am not a physicist by training.