Quantization of massive Dirac neutrinos in external fields

TL;DR

This paper reviews quantum field theory methods for describing massive Dirac neutrinos in external fields, deriving wavefunctions and propagators for neutrinos in matter and magnetic fields, with implications for neutrino oscillations.

Contribution

It provides explicit operator solutions and propagators for massive Dirac neutrinos in external backgrounds, advancing the theoretical framework for neutrino oscillation studies.

Findings

Derived neutrino wavefunctions in matter and magnetic fields.

Obtained the neutrino propagator in a magnetic field.

Confirmed the canonical anticommutation relations for the solutions.

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.