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Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

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  • José Velhinho

Abstract

This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass.

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  • José Velhinho, 2015. "Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-12, October.
    • Handle: RePEc:hin:jnlamp:608940
    DOI: 10.1155/2015/608940
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    Cited by:

    1. José Velhinho, 2017. "Topics of Measure Theory on Infinite Dimensional Spaces," Mathematics, MDPI, vol. 5(3), pages 1-25, August.
    2. 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.

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