Freiburg 2024 – scientific programme
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A: Fachverband Atomphysik
A 31: Atomic Systems in External Fields II
A 31.5: Talk
Thursday, March 14, 2024, 15:30–15:45, HS 1015
Geometric post-Newtonian description of massive spin-half particles in curved spacetime — •Ashkan Alibabaei1,2, Philip Schwartz1, and Domenico Giulini1,3 — 1Institute for Theoretical Physics, Leibniz University Hannover, Appelstraße 2, 30167 Hannover, Germany — 2Institute of Quantum Optics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany — 3Center of Applied Space Technology and Microgravity, University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
The equivalence principle requires matter to universally couple to gravity, encoded in spacetime geometry. For quantum fields, this leads to the framework of quantum field theory in curved spacetime. This framework, however, is quite far detached from the practical description of low-energy quantum systems in terms of Galilei-symmetric Schrödinger equations plus special- and general relativistic corrections. We aim to close this gap by considering the one-particle sector of the respective quantum field theory described effectively by a classical field, for this purpose we apply a systematic low energy approximation scheme. In my talk, I will describe a Hydrogen-like atom coupled to gravity and external electromagnetic field in a twofold expansion scheme, first implementing a weak-gravity approximation, and second a slow velocity post-Newtonian expansion. This yields to a systematic and complete generation of general-relativistic correction terms for spin-half quantum systems. We find new terms that were overlooked in the literature and extend the level of approximation.
Keywords: Quantum matter in gravity; Dirac equation; Post-Newtonian expansion; Generalized Fermi normal coordinates; Formal WKB-like expansion