Description
Neutrino oscillation experiments presently suggest that neutrinos have
a small but finite mass. This paper will discuss how the E(2)-like
subgroup of SL(2,c) can be used to distinguish between massive and
massless particles. We will derive a representation of the SL(2,c)
group which separates out the two sets of spinors contained therein. One 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-1/2 non-zero mass particles. If we renormalize the large components, these gauge-invariant spinors again represent the polarization of neutrinos. If neutrinos are to have mass, then they should not be invariant under gauge transformations.
Primary author
Prof.
Marilyn E. Noz
(New York University)
Co-author
Prof.
Young S. Kim
(University of Maryland, College Park)
