Unruh's detector in the presence of Lorentz symmetry breaking

TL;DR

This paper explores how Lorentz symmetry breaking affects Unruh's detector, showing that in a causal, energy-positive theory it detects no particles, but detection occurs if energy positivity is violated, highlighting the role of causality and energy conditions.

Contribution

It introduces a Lorentz non-invariant quantum field model with a nonlinear dispersion relation and analyzes the detector response under causality and energy positivity constraints.

Findings

No particle detection in causal, energy-positive theories.

Particle detection occurs when energy positivity is violated.

Causality and energy conditions critically influence detector responses.

Abstract

We investigate the quantum field theory of a Lorentz non-invariant model with a massive nonlinear dispersion relation in Minkowski space. The model involves some non-causal signals in the form of wave packets propagating with super-luminal group velocities. To avoid the problems with causality we characterize the causal sector of the theory by a cutoff condition excluding all super-luminal group velocities. It is argued that in the causal theory satisfying the energy positivity condition an Unruh's detector moving with a constant velocity with respect to the preferred frame does not detect any particle. But in a causal theory violating energy positivity, detection of a field quanta occurs. We comment on the origin of this particle creation.