  A four dimensional systematic mathematical approach for investigating
propagation and coupling of wave modes in a slowly varying (in all space
directions and time) anisotropic, absorbing plasma is represented. The
formalism is especially useful for energy considerations of the waves. It is
applicable to general cases of mode conversion in plasmas with general
geometries of space-time and magnetic field configurations. A simple example of
how this formalism can be applied to practical cases is given.
