1 0 0 0 OA Inequivalent Representation of Canonical Commutation Relations in Relation to Casimir Effect
- 著者
- Arai Asao
- 出版者
- Department of Mathematics, Hokkaido University
- 雑誌
- Hokkaido University Preprint Series in Mathematics
- 巻号頁・発行日
- vol.1118, pp.1-23, 2018-10-23
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.
- 著者
- Arai Asao
- 出版者
- 京都大学数理解析研究所
- 雑誌
- 数理解析研究所講究録 (ISSN:18802818)
- 巻号頁・発行日
- vol.2123, pp.101-117, 2019-08
The Casimir effect in the case of a quantum scalar field is considered in view of representation theory of canonical commutation relations (CCR) with infinite degrees of freedom. It is shown that a very singular irreducible representation of the CCR over an inner product space mathscr{E} is associated with the Casimir effect and it is inequivalent to the Fock representation ofthe CCR over mathscr{E}.