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http://hdl.handle.net/10016/6846
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| Title: | Twisted duality of the CAR-algebra |
| Author(s): | Baumgärtel, Hellmut
Jurke, Matthias
Lledó, Fernando |
| Publisher: | American Institute of Physics |
| Issued date: | Aug-2002 |
| Citation: | Journal of Mathematical Physics, 2002, vol. 43, n. 8, p. 4158-4179 |
| URI: | http://hdl.handle.net/10016/6846 |
| ISSN: | 0022-2488 (Print)
1089-7658 (Online) |
| DOI: | 10.1063/1.1483376 |
| Description: | 22 pages, no figures.-- MSC2000 codes: 46L05, 46L65.-- PACS nr.: 02.10.-v.
MR#: MR1915649 (2003d:46067)
Zbl#: Zbl 1060.46040 |
| Abstract: | We give a complete proof of the twisted duality property M(q)'= Z M(q perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use modular theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof. As a byproduct of the proof we obtain an explicit and simple formula for the graph of the modular operator. This formula can be also applied to fermionic free nets, hence giving a formula of the modular operator for any double cone. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1063/1.1483376 |
| Keywords: | Hilbert spaces
Algebra
[PACS] Mathematical methods in physics: Logic, set theory, and algebra |
| Rights: | © American Institute of Physics |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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