Covariant Fermionic Fields of Space-like Particles

TL;DR

This paper develops a covariant formalism for fermionic space-like particles, specifically tachyons, demonstrating their relativistic covariance, localizability, causality, and deriving a modified Dirac equation with an extra helicity term.

Contribution

It introduces a covariant framework for fermionic space-like particles, including tachyons, and extends the Dirac equation to incorporate helicity for such particles.

Findings

Established relativistic covariance of fermionic space-like fields

Demonstrated localizability and causality of tachyons using anticommutators

Derived a modified Dirac equation with an additional helicity term

Abstract

We develop covariant fermionic fields of space-like particles. As an application of the formalism we discuss the example of superluminous tachyons with imaginary rest mass and spin 1/2 forming fermionic ensembles that is relativistically covariant. We use the tachyonic single particle Hilbert space to build the quantum stochastic fields as this notion is more consensual, instability in vacuum quantum field than faster than light particles, in field theory with applications to superconductivity via tachyonic condensation. We also establish the localizability and as a consequence the causality of tachyons (in terms of anticommutators) using the systems of imprimitivity framework and derive the Dirac equation for the space-like particle that has an additional helicity term.