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A coupling prescription for post-Newtonian corrections in quantum mechanics
Univ Edinburgh, Sch Math, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Scotland.;Univ Edinburgh, Maxwell Inst Math Sci, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Scotland..
Univ Edinburgh, Sch Math, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Scotland.;Univ Edinburgh, Maxwell Inst Math Sci, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Scotland..
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Univ Copenhagen, Niels Bohr Inst, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark..ORCID iD: 0000-0003-4947-8526
Stevens Inst Technol, Dept Phys & Engn Phys, Hoboken, NJ 07030 USA.;Stockholm Univ, Albanova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden..
2024 (English)In: SciPost Physics, E-ISSN 2542-4653, Vol. 16, no 3, article id 088Article in journal (Refereed) Published
Abstract [en]

The interplay between quantum theory and general relativity remains one of the main challenges of modern physics. A renewed interest in the low -energy limit is driven by the prospect of new experiments that could probe this interface. Here we develop a covariant framework for expressing post -Newtonian corrections to Schr & ouml;dinger's equation on arbitrary gravitational backgrounds based on a 1/c2 expansion of Lorentzian geometry, where c is the speed of light. Our framework provides a generic coupling prescription of quantum systems to gravity that is valid in the intermediate regime between Newtonian gravity and General Relativity, and that retains the focus on geometry. At each order in 1/c2 this produces a nonrelativistic geometry to which quantum systems at that order couple. By considering the gauge symmetries of both the nonrelativistic geometries and the 1/c2 expansion of the complex Klein-Gordon field, we devise a prescription that allows us to derive the Schr & ouml;dinger equation and its post -Newtonian corrections on a gravitational background order -by -order in 1/c2. We also demonstrate that these results can be obtained from a 1/c2 expansion of the complex Klein-Gordon Lagrangian. We illustrate our methods by performing the 1/c2 expansion of the Kerr metric up to O(c-2), which leads to a special case of the Hartle-Thorne metric. The associated Schr & ouml;dinger equation captures novel and potentially measurable effects.

Place, publisher, year, edition, pages
Stichting SciPost , 2024. Vol. 16, no 3, article id 088
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URN: urn:nbn:se:kth:diva-346090DOI: 10.21468/SciPostPhys.16.3.088ISI: 001208809300001Scopus ID: 2-s2.0-85189310054OAI: oai:DiVA.org:kth-346090DiVA, id: diva2:1855806
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QC 20240503

Available from: 2024-05-03 Created: 2024-05-03 Last updated: 2024-05-03Bibliographically approved

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Obers, Niels A.

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