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

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 Schrödinger-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.

References in corpus (11)

• The Unruh effect and its applications
• Measurement of quantum states of neutrons in the Earth's gravitational field
• Study of the neutron quantum states in the gravity field
• A quantum mechanical description of the experiment on the observation of gravitationally bound states
• The Dirac equation in general relativity, a guide for calculations
• Observation of the Spatial Distribution of Gravitationally Bound Quantum States of Ultracold Neutrons and Its Derivation Using the Wigner Function
• Nonrelativistic Limit of the Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin-Orbit Coupling
• Zeros of the Macdonald function of complex order
• Obtaining the Non-relativistic Quantum Mechanics from Quantum Field Theory: Issues, Folklores and Facts
• Relativistic quantum bouncing particles in a homogeneous gravitational field
• Precision Measurement of the Position-space Wave Functions of Gravitationally Bound Ultracold Neutrons

Cited by in corpus (5)

• Minkowski vacuum in Rindler spacetime and Unruh thermal state for Dirac fields
• Frame-dependence of the non-relativistic limit of quantum fields
• Limits to the observation of the Unruh radiation via first-quantized hydrogen-like atoms
• Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime
• Localization in Quantum Field Theory for inertial and accelerated observers