Abstract
We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We achieved 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.
Highlights
The antineutrino could be a direct consequence of the “tachyoneity” of neutrinos at the free level
Because the tachyon kinematics in the preferred frame scenario as well as the construction of the corresponding quantum field theory is not widely known, we present our approach with necessary details, restricting ourselves to one neutrino generation for simplicity
In order to achieve that and to avoid causal problems with tachyons, existence of a preferred frame must be assumed; it is natural to suppose that the PF coincides with the Cosmic Neutrino Background frame
Summary
It was shown [14] that an approach involving the notion of a preferred frame (PF) allows to construct a Lorentz-covariant quantum field-theoretical model of a relativistic helicity-. In this way one can avoid the fundamental difficulties related to the lack of a finite lower energy limit, appearance of infinite spin multiplets and causal problems appearing in the standard attempts to describe tachyons. 2. In the present paper we formulate a fully consistent quantum field theory of the space-like neutrino with both onehalf helicity components under the assumption of the existence of the preferred frame. Because the tachyon kinematics in the preferred frame scenario as well as the construction of the corresponding quantum field theory is not widely known, we present our approach with necessary details, restricting ourselves to one neutrino generation for simplicity
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