Spectral representation of neutrino propagator in media and off-shell spin properties

TL;DR

This paper develops a spectral representation for neutrino propagators in media and magnetic fields, revealing a polarization axis that simplifies the classification of eigenvalues and dispersion laws based on spin projection.

Contribution

It introduces a spectral representation framework that accounts for media and magnetic field effects on neutrino propagators, highlighting a specific polarization axis for spin classification.

Findings

Eigenvalues classified by spin projection on a definite axis

Dispersion laws depend on polarization states

Spectral representation applicable in media and magnetic fields

Abstract

We construct a spectral representation of neutrino propagator in matter moving with constant velocity, or in constant homogenious magnetic field. In both cases there exists definite 4-axis $z$ of complete polarization, such that corresponding spin projectos commute with propagator. As a result, all eigenvalues of propagator and dispersion laws are classified accoding to spin projection on this axis.