Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

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...

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Main Author: José Velhinho
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/608940
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spelling doaj-a32ded990e724accb52464fc57c161b52021-07-02T07:48:50ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/608940608940Canonical Quantization of the Scalar Field: The Measure Theoretic PerspectiveJosé Velhinho0Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, PortugalThis 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.http://dx.doi.org/10.1155/2015/608940
collection DOAJ
language English
format Article
sources DOAJ
author José Velhinho
spellingShingle José Velhinho
Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
Advances in Mathematical Physics
author_facet José Velhinho
author_sort José Velhinho
title Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
title_short Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
title_full Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
title_fullStr Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
title_full_unstemmed Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
title_sort canonical quantization of the scalar field: the measure theoretic perspective
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/608940
work_keys_str_mv AT josevelhinho canonicalquantizationofthescalarfieldthemeasuretheoreticperspective
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