Evolution of a dense neutrino gas in matter and electromagnetic field

We describe the system of massive Weyl fields propagating in a background matter and interacting with an external electromagnetic field. The interaction with an electromagnetic field is due to the presence of anomalous magnetic moments. To canonically quantize this system first we develop the classical field theory treatment of Weyl spinors in frames of the Hamilton formalism which accounts for the external fields. Then, on the basis of the exact solution of the wave equation for a massive Weyl field in a background matter we obtain the effective Hamiltonian for the description of spin-flavor oscillations of Majorana neutrinos in matter and a magnetic field. Finally, we incorporate in our analysis the neutrino self-interaction which is essential when the neutrino density is sufficiently high. We also discuss the applicability of our results for the studies of collective effects in spin-flavor oscillations of supernova neutrinos in a dense matter and a strong magnetic field.