# What is the Maxwell equation for a polarised light?

In the Dirac equation for a massless fermion, for example, in the Weyl representation, we can split the equation into two separate equations for left-handed and right-handed electrons. In the Weyl represenation, the spinor is split as $$\psi=(\psi_L,\psi_R)$$

For the Maxwell equation for a massless photon, can we split this into two equations, for each of the two polarizations of light? I'm not sure how one would split the 4-vector potential $$A_\mu$$ into the two polarization states e.g. $$\phi_L$$ and $$\phi_R$$.

Also, is there some operator analagous to the $$\frac{1}{2}(1+\gamma^5)$$ operator for the Dirac equation that gives us one of the two polarization states?