Neutrino quantum states and spin light in matter

On the basis of the exact solutions of the modified Dirac equation for a massive neutrino moving in matter we develop the quantum theory of the spin light of neutrino ($SL\nu$). The expression for the emitted photon energy is derived as a function of the density of matter for different matter compositions. The dependence of the photon energy on the helicities of the initial and final neutrino states is shown explicitly. The rate and radiation power of the $SL\nu$ in matter are obtained with the emitted photon linear and circular polarizations being accounted for. The developed quantum approach to the $SL\nu$ in matter (which is similar to the Furry representation of electrodynamics) can be used in the studies of other processes with neutrinos in the presence of matter