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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jerónimo Cortez & Guillermo A. Mena Marugán & José Velhinho, 2020. "Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology," Mathematics, MDPI, vol. 8(1), pages 1-49, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:115-:d:307814
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    References listed on IDEAS

    as
    1. José Velhinho, 2015. "Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-12, October.
    2. Jerónimo Cortez & Ilda Inácio Rodrigues & Mercedes Martín-Benito & José Velhinho, 2018. "On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW Cosmology," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-7, March.
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