Nonrelativistic limit of QFT in curved spacetime

TL;DR

This paper develops a comprehensive framework for understanding the nonrelativistic limit of quantum field theory in curved and noninertial spacetimes, revealing effects on particles, energies, and localization in accelerated frames.

Contribution

It derives the nonrelativistic limit of quantum fields in curved spacetime from first principles, including effects of acceleration and gravity, and applies it to model accelerated atoms and the Unruh effect.

Findings

Nonrelativistic quantum states can be described by wave functions in curved spacetime.

Frame-dependent vacuum states lead to nonlocal effects in quantum field theory.

Experimental constraints on observing the Unruh effect via atomic detectors are discussed.

Abstract

The formalism of nonrelativistic quantum physics was originally considered in the context of inertial frames. Here, we report on a more general framework that includes noninertial frames and arbitrarily strong gravitational fields. We derive from first principles the nonrelativistic limit of quantum fields in curved spacetime. Unique features and subtleties of the fully covariant theory in curved spacetime affect nonrelativistic quantum systems in accelerated frames when the acceleration is sufficiently high. This includes the frame dependent notion of particles, energies, vacuum states and nonrelativistic conditions. By using the algebraic approach to quantum field theory, we detail these effects in the noninertial nonrelativistic regime. The theoretical framework developed here gives predictions about the phenomenology of nonrelativistic quantum systems that are put in noninertial motion. As an application, we derive the realistic model of accelerated nonrelativistic atoms by using Dirac field theory in Rindler spacetime. We report on the experimental constraints for the indirect observation of the Unruh effect by means of atomic detectors via hyperfine structure. Then, we address the problem of localization of quantum states and observables in inertial and accelerated frames. We show how the Born probabilistic notion emerges in both cases as a consequence of the respective nonrelativistic limit. As a result, we find that nonrelativistic states can be described in terms of wave functions that quantify the probability to find particles in each space position. Also, we report on nonlocal effects that originate from the frame dependent nature of vacuum states and nonrelativistic conditions in the quantum field theory in curved spacetime.