Tachyons and the preferred frames

TL;DR

This paper develops a quantum field theory framework for space-like particles (tachyons) that preserves Lorentz symmetry but introduces a preferred frame via synchronization choices, potentially allowing neutrinos to be fermionic tachyons.

Contribution

It proposes a consistent field theory for tachyons with helicity labels, breaking relativity but maintaining Lorentz invariance, and suggests neutrinos could be fermionic tachyons.

Findings

Tachyons are associated with $SO(2)$ little group orbits, labeled by helicity.

A Dirac-like equation for tachyons is shown to be consistent in this framework.

The theory supports the possibility of neutrinos as fermionic tachyons.

Abstract

Quantum field theory of space-like particles is investigated in the framework of absolute causality scheme preserving Lorentz symmetry. It is related to an appropriate choice of the synchronization procedure (definition of time). In this formulation existence of field excitations (tachyons) distinguishes an inertial frame (privileged frame of reference) via spontaneous breaking of the so called synchronization group. In this scheme relativity principle is broken but Lorentz symmetry is exactly preserved in agreement with local properties of the observed world. 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. The cases of the helicity $\lambda = 0$ and $\lambda = \pm\frac{1}{2}$ are investigated in detail and a corresponding consistent field theory is proposed. In particular, it is shown that the Dirac-like equation proposed by Chodos 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 might be fermionic tachyons as it is suggested by experimental data about neutrino masses.