Riemann–Silberstein vector

Summary

The Riemann–Silberstein vector is the complex vector field $F = E + i c B$ built from the electric field and the magnetic field. In terms of it, the four source-free Maxwell's equations become two equations for one complex field. The duality rotations become multiplication of $F$ by a phase, and the energy density becomes $\frac{\varepsilon_0}{2} \abs{F}^2$. It is used to write Maxwell's equations in a form close to the Schrödinger equation, as a wave equation for the photon.