Quantum theory of natural circular, magneto-chiral and non-reciprocal linear dichroism

For dichroic signals produced by parity-odd absorption events, we expose, in correct and concise form, electron degrees of freedomthat participate in correlations between spin and orbital variables. Additionally, and for the first time, we prove sum rules for integrated dichroic signals, analogous to the celebrated work by Thole et al (1992 Phys. Rev. Lett. 68 1943) for parity-even events. Natural circular dichroism is a standard method for characterizing chiral materials, and the photon magneto-chiral effect is an important candidate for the origin of the homo-chirality of life.