Quantization of massive Dirac neutrinos in external fields

TL;DR

The paper addresses quantizing a massive Dirac neutrino in external backgrounds to enable a QFT-based description of neutrino oscillations in such fields. It solves the Dirac equation exactly in uniform matter and in a constant magnetic field, derives the corresponding Hamiltonians and energy spectra, and constructs the quantized field with proper anticommutation relations. Key results include the matter spectrum E_sigma = sqrt((p - sigma g/2)^2 + m^2), the magnetic-field spectrum E_zeta = sqrt((S - zeta mu B)^2 + p_3^2) with S = sqrt(m^2 + p_perp^2), and an explicit propagator S(p) in the magnetic background that reduces to the vacuum form in the limit B -> 0. The work provides a robust framework for calculating neutrino oscillations in external fields using exact solutions and propagators, enabling more accurate QFT-based treatments in astrophysical and laboratory contexts.

Abstract

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.