Toward a Quantum Theory of Tachyon Fields

TL;DR

This paper develops a quantum framework for tachyon fields, including wave function expansions, operator rules, and conserved quantities, addressing causality, helicity, and Lorentz invariance issues for faster-than-light particles.

Contribution

It introduces a consistent quantum theory for tachyon fields, including momentum space expansions, operator commutation rules, and interpretations of particle properties.

Findings

Established causality conditions for tachyon fields.

Derived conserved charge and 4-momentum expressions.

Highlighted the role of helicity in tachyon spinor fields.

Abstract

We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between spacetime points separated by a timelike interval. Calculating the conserved charge and 4-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.