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Advances in Mathematical Physics
Volume 2015, Article ID 608940, 12 pages
Research Article

Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal

Received 16 August 2015; Accepted 2 September 2015

Academic Editor: Ivan Avramidi

Copyright © 2015 José Velhinho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.