{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T01:51:52Z","timestamp":1775181112560,"version":"3.50.1"},"reference-count":110,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:00:00Z","timestamp":1578700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["FIS2017-86497-C2-2-P"],"award-info":[{"award-number":["FIS2017-86497-C2-2-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006087","name":"Direcci\u00f3n General de Asuntos del Personal Acad\u00e9mico, Universidad Nacional Aut\u00f3noma de M\u00e9xico","doi-asserted-by":"publisher","award":["IN113618"],"award-info":[{"award-number":["IN113618"]}],"id":[{"id":"10.13039\/501100006087","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000921","name":"European Cooperation in Science and Technology","doi-asserted-by":"publisher","award":["CA16104 GW"],"award-info":[{"award-number":["CA16104 GW"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\u00eetre-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations.<\/jats:p>","DOI":"10.3390\/math8010115","type":"journal-article","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T04:05:51Z","timestamp":1578888351000},"page":"115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9705-6769","authenticated-orcid":false,"given":"Jer\u00f3nimo","family":"Cortez","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3378-9610","authenticated-orcid":false,"given":"Guillermo A.","family":"Mena Marug\u00e1n","sequence":"additional","affiliation":[{"name":"Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid, Spain"}]},{"given":"Jos\u00e9","family":"Velhinho","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias, Universidade da Beira Interior, R. Marqu\u00eas D\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,11]]},"reference":[{"key":"ref_1","unstructured":"Wald, R.M. (1994). Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago University Press."},{"key":"ref_2","unstructured":"Streater, R.F. (1972). Topics in Functional Analysis, Academic Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"R53","DOI":"10.1088\/0264-9381\/21\/15\/R01","article-title":"Background independent quantum gravity: A status report","volume":"21","author":"Ashtekar","year":"2004","journal-title":"Class. Quantum Grav."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rovelli, C. (2004). 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