Are inertial vacua equivalent in Lorentz-violating theories? Does it matter?

TL;DR

This paper investigates the differences between inertial vacua in Lorentz-violating quantum field theories, revealing inequivalence and high-momentum particle perception in different frames, but finds detectors remain unaffected by these effects.

Contribution

It demonstrates the unitarily inequivalent nature of inertial vacua in Lorentz-violating theories and analyzes detector responses, providing insights into their physical implications.

Findings

Inertial vacua are unitarily inequivalent in Lorentz-violating theories.

Different inertial frames perceive vacuum as populated with high-momentum particles.

Unruh-De Witt detectors are insensitive to vacuum differences.

Abstract

Several approaches to quantum gravity suggest violations of Lorentz symmetry as low-energy signatures. This article uses a concrete Lorentz-violating quantum field theory to study different inertial vacua. We show that they are unitarily inequivalent and that the vacuum in one inertial frame appears, in a different inertial frame, to be populated with particles of arbitrarily high momenta. At first sight, this poses a critical challenge to the physical validity of Lorentz-violating theories, since we do not witness vacuum excitations by changing inertial frames. Nevertheless, we demonstrate that inertial Unruh-De Witt detectors are insensitive to these effects. We also discuss the Hadamard condition for this Lorentz-violating theory.