Frame-dependence of the non-relativistic limit of quantum fields

TL;DR

This paper investigates how the non-relativistic limit of quantum fields depends on the observer's frame of reference, revealing frame-dependent particle states and conditions under which different observers agree on particle properties.

Contribution

It demonstrates that the non-relativistic limit of quantum fields is frame-dependent and analyzes the conditions under which inertial and non-inertial observers agree on particle states.

Findings

Non-relativistic particle states are superpositions of relativistic and non-relativistic particles across frames.

Agreement on particle number occurs only at low accelerations in quasi-inertial regimes.

Wave functions are invariant up to coordinate transformations between inertial and quasi-inertial frames.

Abstract

We study the non-relativistic limit of quantum fields for an inertial and a non-inertial observer. We show that non-relativistic particle states appear as a superposition of relativistic and non-relativistic particles in different frames. Hence, the non-relativistic limit is frame-dependent. We detail this result when the non-inertial observer has uniform constant acceleration. Only for low accelerations, the accelerated observer agrees with the inertial frame about the non-relativistic nature of particles locally. In such a quasi-inertial regime, both observers agree about the number of particles describing quantum field states. The same does not occur when the acceleration is arbitrarily large (e.g., the Unruh effect). We furthermore prove that wave functions of particles in the inertial and the quasi-inertial frame are identical up to the coordinate transformation relating the two frames.