{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T17:16:43Z","timestamp":1772558203822,"version":"3.50.1"},"reference-count":11,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T00:00:00Z","timestamp":1772409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ISblue project, Interdisciplinary graduate school","award":["ANR-17-EURE-0015"],"award-info":[{"award-number":["ANR-17-EURE-0015"]}]},{"name":"French government under the program \u201cInvestissements d\u2019Avenir\u201d embedded in France 2030"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Universe"],"abstract":"<jats:p>We extend the representation frame formalism, previously introduced to account for key cosmological observations in the Einstein static universe, to non-relativistic quantum mechanics. In this framework, each inertial observer is associated with a flat representation referential\u00a0Robs, defined as the tangent space to the spatial manifold at the observer\u2019s position, in which all measurements are represented. The Euclidean structure of Robs allows quantum systems to be described using the standard Schr\u00f6dinger formalism, avoiding the technical ambiguities that arise when quantising directly on curved manifolds. We derive the relation between the Hamiltonian governing quantum dynamics in Robs and its counterpart defined on the physical manifold U, and show that curvature effects enter as observer-dependent modifications of effective potentials. Although the resulting quantum description depends on the observer\u2019s representation frame, we show that this does not lead to contradictions between observers: consistency of measurement outcomes follows from the standard structure of quantum correlations established by physical interactions. We illustrate the formalism with explicit applications, including the hydrogen atom in an Einstein static universe and quantum systems in the vicinity of a black hole, highlighting how spacetime curvature manifests itself in the observer\u2019s quantum description.<\/jats:p>","DOI":"10.3390\/universe12030069","type":"journal-article","created":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T15:22:21Z","timestamp":1772551341000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Representation Formalism and Quantum Mechanics in Curved Spacetime"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8960-7279","authenticated-orcid":false,"given":"Th\u00e9ophile","family":"Caby","sequence":"first","affiliation":[{"name":"Laboratoire d\u2019Oc\u00e9anographie Physique et Spatiale (LOPS), Institut Universitaire Europ\u00e9en de la Mer (IUEM), Universit\u00e9 de Bretagne Occidentale, Technop\u00f4le Brest-Iroise, Rue Dumont d\u2019Urville, 29280 Plouzan\u00e9, France"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Caby, T. (2025). On the Observation of Distant Objects in General Relativity and Its Implications in Cosmology. Universe, 11.","DOI":"10.3390\/universe11120384"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1007\/BF01591613","article-title":"Kosmologische Betrachtungen zur allgemeinen Relativitatstheorie","volume":"7","author":"Einstein","year":"1919","journal-title":"Naturwissenschaften"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1103\/RevModPhys.29.377","article-title":"Dynamical theory in curved spaces. I. A review of the classical and quantum action principles","volume":"29","author":"DeWitt","year":"1957","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1143\/PTP.23.1","article-title":"Quantum Mechanics in Curved Space-Time","volume":"23","author":"Misra","year":"1960","journal-title":"Prog. Theor. 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Relativ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1088\/0305-4470\/9\/7\/010","article-title":"Electrostatics and magnetostatics in the Schwarzschild metric","volume":"9","author":"Linet","year":"1976","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Birrell, N.D., and Davies, P.C.W. (1982). Quantum Fields in Curved Space, Cambridge University Press.","DOI":"10.1017\/CBO9780511622632"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Parker, L., and Toms, D. (2009). Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, Cambridge University Press.","DOI":"10.1017\/CBO9780511813924"}],"container-title":["Universe"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-1997\/12\/3\/69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T15:57:05Z","timestamp":1772553425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-1997\/12\/3\/69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,2]]},"references-count":11,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["universe12030069"],"URL":"https:\/\/doi.org\/10.3390\/universe12030069","relation":{},"ISSN":["2218-1997"],"issn-type":[{"value":"2218-1997","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,2]]}}}