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

TL;DR

This paper explores the internal space-time symmetries of massless particles, revealing how gauge invariance leads to neutrino polarization and clarifies the gauge dependence of electromagnetic potentials.

Contribution

It demonstrates that gauge invariance in the little-group framework explains neutrino polarization and the gauge dependence of electromagnetic potentials for massless spin-1/2 particles.

Findings

Dirac equation involves only gauge-invariant spinors

Gauge-dependent spinors cause electromagnetic gauge dependence

Symmetry group for massless particles is a limit of the massive case

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.