Quantization of massive Dirac neutrinos in external fields

We review the applications of the quantum field theory (QFT) for the description of massive Dirac neutrinos in external fields. Two particular cases of external background are considered. First, we examine neutrinos in background matter. Then, we study neutrinos with anomalous magnetic moments in a magnetic field. In both situations, we derive the operator valued neutrino wavefunctions, accounting for external fields, which obey the canonical anticommutation relations. Then, we check that the total energy and momentum of a neutrino field have the appropriate forms. Using the exact solution in a Dirac equation in a magnetic field, we also derive the propagator for a massive Dirac neutrino in this external background. The results obtained are of importance for the QFT application to neutrino oscillations in external fields.