Dynamics of radiation due to vacuum nonlinearities

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.