  We develop the quantum theory of the spin light of neutrino ($SL\nu$) exactly
accounting for the effect of background matter. Contrary to the already
performed studies of the $SL\nu$, in this paper we derive explicit and closed
expressions for the $SL\nu$ 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 $SL\nu$ polarization properties and show
that within a wide range of neutrino momenta and matter densities the $SL\nu$
radiation is circularly polarized. Conditions for effective $SL\nu$ 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 $SL\nu$ production during different astrophysical and
cosmology processes are discussed.
