Gyromagnetic g_s factors of the spin-1/2 particles in the (1/2+,1/2-,3/2-) triad of the four-vector spinor, \psi_\mu, irreducibility, and linearity

Abstract

We show that the spin (1/2-) particle from the (1/2,1)+(1,1/2) Lorentz irreducible sector of the four-vector spinor can not be described within a linear formalism but behaves as a genuinely quadratic fermion satisfying the generalized Feynman-Gell-Mann equation with a gyromagnetic factor of (-2/3). In contrast, spin (1/2 +) from the (1/2,0)+(0,1/2) sector is confirmed as a genuine linear Dirac fermion whose gyromagnetic factor takes the value of two units.We calculate Compton scatterings off each one of the two targets and obtain both times well behaved cross sections in the ultra relativistic limit and in accord with unitarity.