Small-mass Neutrinos, Massless Neutrinos, and Gauge Transformations

Abstract

Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. This paper shows how the Dirac equation can be used to distinguish between massive and massless particles. In the large-momentum/zero mass limit, the Dirac spinors can be separated into large and small components. The large components are gauge invariant, while the small components are not. If we renormalize the large components, these gauge invariant spinors represent the polarization of neutrinos. The small components represent spin- 1 non-zero mass particles. A similar analysis is then done when the neutrino mass is considered as an invariant of the Lorentz transformation. If neutrinos are to have mass, then they should not be invariant under gauge transformations.