Is there a Lagrangian reproducing Maxwell's equations without the use of the scalar and vector potential? Obviously $\mathcal{L} = -\frac14F_{\mu \nu}F^{\mu \nu}$ doesn't work since in terms of $E$ and $B$ fields it doesn't contain timederivatives of those and won't reproduce dynamics.
What I'm looking for is a Lagrangian that reproduces Maxwell equations when varied wrt $E$ and $B$ and does not contain any reference to the unphysical $A^\mu$
