Hamiltonian density of EM fields

I'm learning about the field theory of electromagnetism. The Lagrangian density for an electromagnetic field can be taken to be$$\mathcal{L} = -\frac{1}{4} F^{\mu\nu} F_{\mu\nu} + \mu_0 A^\mu J_\mu$$

such that the Euler-Lagrange equations reproduce the inhomogeneous Maxwell's equations\begin{align*} \partial_\nu F^{\mu\nu} = \partial_\nu \frac{\partial\mathcal{L}}{\partial(\partial_\nu A_\mu)} = \frac{\partial\mathcal{L}}{\partial A_\mu} = \mu_0 J^\mu\end{align*}

Is there a Hamiltonian formalism that gives the same result?