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

Jerónimo Cortez, Guillermo A. Mena Marugán and José Velhinho
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Jerónimo Cortez: Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
Guillermo A. Mena Marugán: Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid, Spain
José Velhinho: Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal

Mathematics, 2020, vol. 8, issue 1, 1-49

Abstract: 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.

Keywords: quantum fields in curved spacetimes; quantum cosmology; Fock quantization; quantum fields in nonstationary settings; uniqueness criteria; unitarity in cosmological backgrounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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