The four states of the Massless neutrino with pauli coupling by Spin-Gauge invariance

Abstract

The Pauli coupling \(a\bar \psi \sigma ^{uv} \psi F_{uv} \) is introduced for four-component neutrino states and related to local T4⊂SU(2,2) spin-gauge (not internal symmetry) transformations applied to the massless Dirac equation. The well-known left-right asymmetry for free neutrino helicity states is generalised and discussed for Pauli-coupled neutrinos. An explicit exact solution is obtained for Pauli-coupled neutrino equations in an external free radiation field by the use of the above local spin-gauge transformations. It is also suggested that local SL(2, C)⊂SU(2,2) spin-gauge transformations can be used to obtain models of neutral currents for neutrinos.