Low energy Lorentz violation from high energy modified dispersion in inertial and circular motion

TL;DR

This paper investigates how high-energy modifications to dispersion relations cause low-energy Lorentz violations for Unruh-DeWitt detectors in inertial and circular motion across various spacetime dimensions, with implications for laboratory observations.

Contribution

It generalizes previous four-dimensional results to arbitrary dimensions and analyzes Lorentz violations in both inertial and circular motions with modified dispersion relations.

Findings

Inertial detectors show large low-energy Lorentz violations in dimensions > 2.

Circular motion detectors exhibit similar violations in three dimensions.

Provides analytic groundwork for studying circular motion in higher dimensions.

Abstract

We consider an Unruh-DeWitt detector in inertial and circular motion in Minkowski spacetime of arbitrary dimension, coupled to a quantised scalar field with the Lorentz-violating dispersion relation $\omega = |{\bf k}|\, f (|{\bf k}|/M_{\star})$, where $M_{\star}$ is the Lorentz-breaking scale. Assuming that $f$ dips below unity somewhere, we show that an inertial detector experiences large low energy Lorentz violations in all spacetime dimensions greater than two, generalising previous results in four dimensions. For a detector in circular motion, we show that a similar low energy Lorentz violation occurs in three spacetime dimensions, and we lay the analytic groundwork for examining circular motion in all dimensions greater than three, generalising previous work by Stargen, Kajuri and Sriramkumar in four dimensions. The circular motion results may be relevant for the prospects of observing the circular motion Unruh effect in analogue laboratory systems.