  In quantum electrodynamics, photon-photon scattering can be the result of the
exchange of virtual electron-positron pairs. This gives rise to a non-trivial
dispersion relation for a single photon moving on a background of
electromagnetic fields. Knowledge of the dispersion relation can be
transferred, using standard methods, into new insights in the dynamical
equations for the photons. Effectively, those equations will contain different
types of self-interaction terms, depending on whether the photons are coherent
or not. It is shown that coherent photons are governed by a nonlinear
Schroedinger type equation, such that the self-interaction terms vanish in the
limit of parallel propagating waves. For incoherent photons, a set of fluid
equations can determine the evolution of the corresponding radiation gas. In
the case of a self-interacting radiation fluid, it is shown that Landau damping
can occur.
