Twisted duality of the CAR-Algebra
Mathematical Physics
2009-11-07 v1 Functional Analysis
math.MP
Operator Algebras
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.
Cite
@article{arxiv.math-ph/0204029,
title = {Twisted duality of the CAR-Algebra},
author = {Hellmut Baumgärtel and Matthias Jurke and Fernando Lledó},
journal= {arXiv preprint arXiv:math-ph/0204029},
year = {2009}
}
Comments
32 pages, Latex2e, to appear in Journal of Mathematical Physics