Stable, Renormalizable, Scalar Tachyonic Quantum Field Theory with Chronology Protection

TL;DR

This paper develops a scalar tachyonic quantum field theory that breaks Lorentz symmetry to ensure renormalizability and causality, providing a consistent model with controlled behavior and chronology protection.

Contribution

It introduces a Lorentz symmetry-breaking scalar tachyonic quantum field model that avoids exponential instabilities and maintains causality, with detailed analysis of its properties.

Findings

Lorentz symmetry breaking is necessary for renormalizable tachyonic QFTs.

The model satisfies the Hadamard condition and preserves causality.

Standard theorems like PCT and spin-statistics are discussed within this framework.

Abstract

We use microlocal arguments to suggest that Lorentz symmetry breaking must occur in a reasonably behaved tachyonic quantum field theory that permits renormalizability. In view of this, we present a scalar tachyonic quantum field model with manifestly broken Lorentz symmetry and without exponentially growing/decaying modes. A notion of causality, in which anti-telephones are excluded, and which is viewed as a form of chronology protection, is obeyed. The field theory is constructed in a preferred tachyon frame in terms of commuting creation/annihilation operators. We calculate some sample (renormalized) operators in this preferred frame, argue that the Hadamard condition is satisfied, and discuss the PCT and spin-statistics theorems for this model.