  In this work we include the elastic scattering of longitudinal
electromagnetic waves in transport theory using a medium filled with
point-like, electric dipoles. The interference between longitudinal and
transverse waves creates two new channels among which one allows energy
transport. This picture is worked out by extending the independent scattering
framework of radiative transfer to include binary dipole-dipole interactions.
We calculate the diffusion constant of light in the new transport channel and
investigate the role of longitudinal waves in other aspects of light diffusion
by considering the density of states, equipartition, and Lorentz local field.
In the strongly scattering regime, the different transport mechanisms couple
and impose a minimum conductivity of electromagnetic waves, thereby preventing
Anderson localization of light in the medium. We extend the self-consistent
theory of localization and compare the predictions to extensive numerical
simulations.
