  We performed a Lorentz covariant quantization of the spin-1/2 fermion field
assuming the space-like energy-momentum dispersion relation. We a\-chieved the
task in the following steps: ($i$) determining the unitary realizations of the
inhomogenous Lorentz group in the preferred frame scenario by means of the
Wigner-Mackey induction procedure and constructing the Fock space; ($ii$)
formulating the theory in a manifestly covariant way by constructing the field
amplitudes according to the Weinberg method; ($iii$) obtaining the final
constraints on the amplitudes by postulating a Dirac-like free field equation.
Our theory allows to predict all chiral properties of the neutrinos, preserving
the Standard Model dynamics. We discussed the form of the fundamental
observables, energy and helicity, and show that non-observation of the
$+\tfrac{1}{2}$ helicity state of the neutrino and the $-\tfrac{1}{2}$ helicity
state of the antineutrino could be a direct consequence of the "tachyoneity" of
neutrinos at the free level. We found that the free field theory of the
space-like neutrino is not invariant under the C and P transformations
separately but is CP-invariant. We calculated and analyzed the electron energy
spectrum in tritium decay within the framework of our theory and found an
excellent agreement with the recent measurement of KATRIN. In our formalism the
questions of negative/imaginary energies and the causality problem does not
appear.
