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Open AccessArticle

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

1
Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
2
Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid, Spain
3
Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 115; https://doi.org/10.3390/math8010115
Received: 9 December 2019 / Revised: 3 January 2020 / Accepted: 7 January 2020 / Published: 11 January 2020
(This article belongs to the Special Issue Mathematical and Computational Cosmology)
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-Lemaître-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. View Full-Text
Keywords: quantum fields in curved spacetimes; quantum cosmology; Fock quantization; quantum fields in nonstationary settings; uniqueness criteria; unitarity in cosmological backgrounds quantum fields in curved spacetimes; quantum cosmology; Fock quantization; quantum fields in nonstationary settings; uniqueness criteria; unitarity in cosmological backgrounds
MDPI and ACS Style

Cortez, J.; Mena Marugán, G.A.; Velhinho, J. Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology. Mathematics 2020, 8, 115.

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