A new derivation of the transfer equation for polarized radiation under non-LTE conditions in a magnetic field. I - Formalism

Quantum electrodynamics principles are employed in a study of stellar atmospheres in order to model stellar magnetic fields under conditions lacking local thermodynamic equilibrium. The temporal evolution of the Stokes vector is calculated in order to derive its transfer equation along with a formalism for radiative diffusion. The formalism is developed through use of a method of a density operator, with a probability included that the system will have a particular density at any one time. Specific attention is given to the interaction of radiation and an atom, which results in a perturbation. An initial state is defined from which the evolution of the density matrix can proceed.