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Inequivalent Representation of Canonical Commutation Relations in Relation to Casimir Effect
Title: | Inequivalent Representation of Canonical Commutation Relations in Relation to Casimir Effect |
Authors: | Arai, Asao1 Browse this author →KAKEN DB |
Authors(alt): | 新井, 朝雄1 |
Keywords: | Casimir effect | canonical commutation relations | inequivalent representation | Boson Fock space | singular Bogoliubov transformation | quantum scalar field |
Issue Date: | 23-Oct-2018 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 1118 |
Start Page: | 1 |
End Page: | 23 |
Abstract: | It is shown that an irreducible representation of the CCR over a dense subspace of a boson Fock space is associated with a quantum system whose space configuration may give rise to Casimir effect in the context of a quantum scalar field and that it is inequivalent to the Fock representation of the same CCR. A quantum scalar field is constructed from the representation. A new feature of the analysis is to treat a singular Bogoliubov transformation, which is different from the usual bosonic Bogoliubov transformation and from which the inequivalent irreducible representation of the CCR is constructed. |
Description: | Mathematics Subject Classification 2010: 81R10, 47L60. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/71731 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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