Are Neutrinos Spinorial Tachyons?

Abstract

Quantum field theory of space-like particles is investigated in the framework of absolute causality scheme preserving Lorentz symmetry. It is shown that tachyons are associated with unitary orbits of Poincar\'e mappings induced from SO(2) little group instead of SO(2,1) one. Therefore the corresponding elementary states are labelled by helicity. A particular case of the helicity $\lambda=\pm{1/2}$ is investigated in detail and a corresponding consistent field theory is proposed. In particular, it is shown that the Dirac-like equation proposed by Chodos {\it et al}., inconsistent in the standard formulation of QFT, can be consistently quantized in the presented framework. This allows us to treat more seriously possibility that neutrinos can be fermionic tachyons as it is suggested by the present experimental data about neutrino masses.