Quantization of the tachyonic field and the preferred frame

TL;DR

This paper proposes a quantization scheme for imaginary-mass fields that maintains Lorentz covariance and causality, introduces a preferred frame via spontaneous symmetry breaking, and explores implications for tachyonic excitations.

Contribution

It introduces a novel quantization approach for tachyonic fields that preserves Lorentz symmetry while allowing a preferred frame through synchronization group breaking.

Findings

Maintains Lorentz covariance and causality in tachyon quantization.

Identifies a preferred inertial frame via spontaneous symmetry breaking.

Shows Lorentz symmetry is preserved despite a preferred frame.

Abstract

A consistent quantization scheme for imaginary-mass field is proposed. It is related to an appropriate choice of the synchronization procedure (definition of time), which guarantee an absolute causality in agreement with Lorentz covariance. In that formulation a possible existence of field excitations (tachyons) distinguish an inertial frame (tachyon privileged frame of reference) {\em 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.