General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles

• URL: http://arxiv.org/abs/2411.14307v1
• Date: Thu, 21 Nov 2024 17:00:00 GMT
• Title: General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles
• Authors: Gregor Janson, Richard Lopp,
• Abstract summary: atom interferometric models often include relativistic effects only in an ad hoc fashion. We generalize special-relativistic center of mass and relative coordinates to obtain light-matter dynamics in curved spacetime. We obtain the Hamiltonian of a fully first-quantized two-particle atom interacting with the electromagnetic field in curved spacetime.
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• Abstract: Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the multi-particle nature of quantum-delocalizable atoms in curved spacetime and generalize the special-relativistic center of mass (COM) and relative coordinates that have previously been studied for Minkowski spacetime to obtain the light-matter dynamics in curved spacetime. In particular, for a local Schwarzschild observer located at the surface of the Earth using Fermi-Walker coordinates, we find gravitational correction terms for the Poincar\'e symmetry generators and use them to derive general relativistic COM and relative coordinates. In these coordinates we obtain the Hamiltonian of a fully first-quantized two-particle atom interacting with the electromagnetic field in curved spacetime that naturally incorporates special and general relativistic effects.

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