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

TL;DR

This paper investigates the gyromagnetic g_s factors of spin-1/2 particles in different sectors of the four-vector spinor, revealing that the (1/2-) sector behaves as a quadratic fermion with a specific g_s, while the (1/2+) sector is a linear Dirac fermion with g_s=2.

Contribution

It demonstrates that the (1/2-) particle cannot be described linearly and behaves as a quadratic fermion, contrasting with the linear Dirac behavior of the (1/2+) particle, with implications for their electromagnetic interactions.

Findings

(1/2-) particle has g_s = -2/3 and behaves as a quadratic fermion.

(1/2+) particle is a linear Dirac fermion with g_s = 2.

Both particles produce well-behaved Compton scattering cross sections.

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.