Neutrino propagation in media and axis of complete polarization

TL;DR

This paper develops a spectral representation of neutrino propagators in media and magnetic fields, identifying a polarization axis that simplifies the eigenvalue problem and classifies dispersion laws by spin projection.

Contribution

It introduces a fixed polarization axis in media and magnetic fields, enabling a simplified spectral representation of neutrino propagators and classification of dispersion laws.

Findings

Eigenvalues classified by spin projection on a fixed axis

Spectral representation analogous to vacuum propagator

Simplified eigenvalue problem for neutrino in media

Abstract

We construct a spectral representation of neutrino propagator in moving matter or in external magnetic field. In both cases there exists fixed four-dimensional axis of polarization, such that the corresponding spin projectors commute with propagator. As a result, all eigenvalues of propagator and, consequently, dispersion laws for neutrino in media are classified according to spin projection onto this axis. Use of the found spin projectors simplifies essentially the eigenvalue problem and allows to build spectral representation of propagator in moving matter or external magnetic field in analogy with the vacuum propagator.