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

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.