Lorentz-invariant and Lorentz-non-invariant aspects of a scalar tachyon field Lagrangian and the scalar tachyon Feynman propagator

TL;DR

This paper explores a Lorentz-covariant approach to scalar tachyon quantum field theory, emphasizing the role of a preferred reference frame to maintain causality, and analyzes Lorentz-invariant equations and propagators within a Lorentz-violating framework.

Contribution

It introduces a Lorentz-covariant Lagrangian for scalar tachyons that maintains Lorentz-invariant equations and propagators despite Lorentz symmetry being covariantly broken.

Findings

Equation of motion is Lorentz-invariant

Feynman propagator is Lorentz-invariant

Lorentz symmetry is covariantly broken

Abstract

A consistent theory of faster-than-light particles (tachyons) can be built replacing the standard Lorentz-invariant approach to the quantum field theory of tachyons by the Lorentz-covariant one, invoking a concept of the preferred reference frame. This is a mandatory condition imposed by the causality conservation. In this article some features of a Lorentz-violating (but Lorentz-covariant) Lagrangian of a scalar tachyon field are considered. It is shown that the equation of motion and Feynman propagator resulting from it are Lorentz-invariant, while the Lorentz symmetry of the suggested tachyon field model can be defined as covariantly broken.