A quasi-classical method for deriving the equations of radiative transfer in a magnetic field

A new derivation of the matrix equations of radiative transfer in a magnetic field is presented, which is based on the classical approach of M. Born and V.E. Stepanov. Convenient vector relations making it possible to formulate the radiative-transfer equations in an arbitrary coordinate system and choose a convenient system of Stokes parameters are presented. The cases of the solar atmosphere and a stellar atmosphere with a dipolar magnetic field are presented as examples. The use of the radiative-transfer equations written in terms of two main oscillation components (the method of V.E. Stepanov) can lead to crude errors when the complex nature of the absorption coefficients is taken into account.