Geometric post-Newtonian description of massive spin-half particles in curved spacetime

authored by

Ashkan Alibabaei, Philip K. Schwartz, Domenico Giulini

Abstract

We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline \(\gamma\) representing a classical clock. We use generalised Fermi normal coordinates in a tubular neighbourhood of \(\gamma\) and expand the Dirac equation up to, and including, the second order in the dimensionless parameter given by the ratio of the geodesic distance to the radii defined by spacetime curvature, linear acceleration of \(\gamma\), and angular velocity of rotation of the employed spatial reference frame along \(\gamma\). With respect to the time measured by the clock \(\gamma\), we compute the Dirac Hamiltonian to that order. On top of this `weak-gravity' expansion we then perform a post-Newtonian expansion up to, and including, the second order of \(1/c\), corresponding to a `slow-velocity' expansion with respect to \(\gamma\). As a result of these combined expansions we give the weak-gravity post-Newtonian expression for the Pauli Hamiltonian of a spin-half particle in an external electromagnetic field. This extends and partially corrects recent results from the literature, which we discuss and compare in some detail.

Organisation(s)

CRC 1227 Designed Quantum States of Matter (DQ-mat)
Institute of Quantum Optics
Institute of Theoretical Physics
QuantumFrontiers

External Organisation(s)

Center of Applied Space Technology and Microgravity (ZARM)
University of Bremen

Type

Article

Journal

Classical and Quantum Gravity

Volume

40

ISSN

0264-9381

Publication date

07.11.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Electronic version(s)

https://arxiv.org/abs/2307.04743 (Access: Open)
https://doi.org/10.1088/1361-6382/ad079c (Access: Open)