Non-relativistic limit of scalar and Dirac fields in curved spacetime

TL;DR

This paper derives the non-relativistic limits of scalar and Dirac fields in curved spacetime to identify general relativistic corrections to quantum particles under gravity, highlighting the potential for experimental detection of non-Newtonian effects.

Contribution

It provides a rigorous derivation of relativistic corrections to quantum theory in curved spacetime, emphasizing differences between scalar and Dirac fields in gravitational contexts.

Findings

Dirac particles are more suitable for observing non-Newtonian gravity effects.

Gravity-spin coupling becomes significant at high accelerations.

Non-inertial observers can distinguish scalar from Dirac fields via particle-gravity interactions.

Abstract

We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays experimentally accessible. We believe that the ever-improving measurement accuracy and the theoretical interest in finding general relativistic effects in quantum systems require the introduction of corrections to the Schr\"{o}dinger-Newtonian theory. We rigorously determine these corrections by the non-relativistic limit of fully relativistic quantum theories in curved spacetime. For curved static spacetimes, we show how a non-inertial observer (equivalently, an observer in the presence of a gravitational field) can distinguish a scalar field from a Dirac field by particle-gravity interaction. We study the Rindler spacetime and discuss the difference between the resulting non-relativistic Hamiltonians. We find that for sufficiently large acceleration, the gravity-spin coupling dominates over the corrections for scalar fields, promoting Dirac particles as the best candidates for observing non-Newtonian gravity in quantum particle phenomenology.