Gauge Transformations on Massless Spin-1/2 Particles and Neutrino Polarization as a Consequence of Gauge Invariance

Abstract

The two-by-two representation of the SL(2,c) group is for spin-1/2 particles. Starting from this two-by-two representation, it is possible to construct the four-by-four matrices for spin-1 particles. For massless particles, it is possible to construct four-potentials from two-component SL(2,c) spinors. Four potentials are subject to gauge transformations and are gauge-dependent. Then this gauge dependence necessarily comes from the two-component spinors which make up the four-potential. Then there must be a gauge-dependent spinor. This gauge-dependent spinor is discussed in detail. It is shown that neutrino polarization is a consequence of gauge invariance applicable to the two-by-two representation of the SL(2,c) group.