Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interprete...

We introduce a new notion of “matrix potential” to nonlinear optical systems. In terms of a matrix potential g, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multi-level media. We show that the Bloch part of the equation can solved identically through g and the remainin...

We show that the Maxwell equations in vacuum and the Dirac equation without the mass term are special cases of the Fueter-Lanczos conditions. .