Phase space formulation of radiative transfer in optically thick plasmas

We present a formulation of the radiative transfer theory based on the quantum phase space formalism. The formalism employs the Wigner function relative to the electric field in (r,t,k,ω) space. It is shown that this quantity obeys a transport equation with source and loss terms nonlocal in space and time. This delocalization is a feature of the Heisenberg uncertainty relation, both relative to position and momentum and to time and energy. A discussion of the theory, together with links to the standard radiative transfer formalism, is done.