Internal Space-time Symmetries of Massless Particles and Neutrino Polarization as a Consequence of Gauge Invariance

Abstract

There are gauge-transformation operators applicable to massless spin-1/2 particles within the little-group framework of internal space-time symmetries of massive and massless particles. It is shown that two of the $SL(2,c)$ spinors are invariant under gauge transformations while the remaining two are not. The Dirac equation contains only the gauge-invariant spinors leading to polarized neutrinos. It is shown that the gauge-dependent $SL(2,c)$ spinor is the origin of the gauge dependence of electromagnetic four-potentials. It is noted also that, for spin-1/2 particles, the symmetry group for massless particles is an infinite-momentum/zero-mass limit of the symmetry group for massive particles.

Comments: Latex 9 pages, 2 epsfigs, based on one of the lectures delivered at the Advanced Study Institute on Symmetries and Spin (Prague, Czech Republic, July 2001)