Do Small-mass Neutrinos participate in Gauge Transformations?

Abstract

Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. If neutrinos are to have mass, there should be a Lorentz frame in which they can be brought to rest. This paper discusses how Wigner's little groups can be used to distinguish between massive and massless particles. We derive a representation of the SL(2,c) group which separates out the two sets of spinors contained therein. One set is gauge dependent. The other set is gauge-invariant and represents polarized neutrinos. We show that a similar calculation can be done for the Dirac equation. 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. These small components represent spin-$\frac{1}{2}$ non-zero mass particles. If we renormalize the large components, these gauge invariant spinors again represent the polarization of neutrinos. Massive neutrinos cannot be invariant under gauge transformations.