Quantum theory of neutrino spin light in dense matter

We develop the quantum theory of the spin light of neutrino (SLν) exactly accounting for the effect of background matter. Contrary to the already performed studies of the SLν, in this Letter we derive expressions for the SLν rate and power and for the emitted photon energy, which are valid for an arbitrary matter density (including very high values). The spatial distribution of the radiation power and the dependence of the emitted photon energy on the direction of radiation are also studied in detail for the first time. We analyze the SLν polarization properties and show that within a wide range of neutrino momenta and matter densities the SLν radiation is circularly polarized. Conditions for effective SLν photon propagation in the electron plasma are discussed. It is also shown that in dense matter the average energy of the emitted photon can reach values in the range from one third of the neutrino momentum up to one half of the neutrino energy in matter. The main features of the studied radiation are summarized, and possibilities for the SLν production during different astrophysical and cosmology processes are discussed.