Geometric postNewtonian description of massive spinhalf 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 fourdimensional 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 `weakgravity' expansion we then perform a postNewtonian expansion up to, and including, the second order of \(1/c\), corresponding to a `slowvelocity' expansion with respect to \(\gamma\). As a result of these combined expansions we give the weakgravity postNewtonian expression for the Pauli Hamiltonian of a spinhalf 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 (DQmat)
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
 02649381
 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/10.1088/13616382/ad079c (Access: Open)