Interactions in noncommutative dynamics
arXiv:math/9910167 · doi:10.1007/s002200050802
Abstract
A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal B(H)$ 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.
22 pages. Replacement corrects misnumbering of formulas in section 4. No change in mathematical content