Interactions in noncommutative dynamics
Operator Algebras
2009-10-31 v3
Abstract
A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of endowed with a certain causal structure. With any interaction there is a well-defined "state of the past" and a well-defined "state of the future". We describe the construction of many interactions involving cocycle perturbations of the CAR/CCR flows and show that they are nontrivial. The proof of nontriviality is based on a new inequality, relating the eigenvalue lists of the "past" and "future" states to the norm of a linear functional on a certain C^*-algebra.
Cite
@article{arxiv.math/9910167,
title = {Interactions in noncommutative dynamics},
author = {William Arveson},
journal= {arXiv preprint arXiv:math/9910167},
year = {2009}
}
Comments
22 pages. Replacement corrects misnumbering of formulas in section 4. No change in mathematical content