A new theory of magneto-optical conductivity utilizing state-independent projectors in a continued fraction scheme

Starting with a magneto-optical conductivity equation originally based on t he Liouville equation formalism and with the use of state-independent proje ctors, we obtain a continued fraction expression generated by the current o perator and the Lionville operator. All the members of the relaxation funct ion appear to be calculated separately, which helps adopt Matthiessen's rul e in some limited cases. Furthermore, the mathematical tools developed in t he traditional continued fraction and recurrence relation schemes are shown to be applicable to the present system.