  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
interpreted as photon wave functions, are given both for plane waves and for
angular-momentum eigenstates. Rotationally invariant projection operators are
used to identify transverse or longitudinal electric and magnetic fields. For
plane waves, the velocity transformed transverse wave functions are also
transverse, and the velocity transformed longitudinal wave functions include
both longitudinal and transverse components. A suitable sum over these
eigenfunctions provides a Green function for the matrix Maxwell equation, which
can be expressed in the same covariant form as the Green function for the Dirac
equation. Radiation from a dipole source and from a Dirac atomic transition
current are calculated to illustrate applications of the Maxwell Green
function.
