How to implant a causal $\Theta$ function into a tachyon field operator, or why tachyons do not violate causality

TL;DR

This paper proposes a Lorentz-covariant method to incorporate a causal $ heta$ function into tachyon quantum field operators, ensuring causality and preventing causal loops in faster-than-light particle theories.

Contribution

It introduces a Lorentz-covariant way to embed a causal $ heta$ function into tachyon field operators, maintaining causality in quantum theories of tachyons.

Findings

A causal $ heta$ function can be Lorentz-covariantly integrated into tachyon fields.

The approach prevents causal loops caused by faster-than-light signals.

Ensures causality in quantum tachyon theories.

Abstract

The postulate of the preferred reference frame in which the signal propagation is governed by retarded causality is a must for any theory of faster-than-light particles and signals. Such a system does exist and is the comoving system of the relativistic cosmology. Restrictions imposed by the causality conservation can be expressed via a causal $\Theta$ function assumed to be acting in both, the classical and quantum field theories of tachyons. A Lorentz-covariant introduction of this $\Theta$ function, which ensures a causal behaviour of real tachyons (asymptotic tachyon states) preventing the appearance of causal loops constructed with the use of faster-than-light particles and signals, into the tachyon quantum field operators is suggested.