Interactions in noncommutative dynamics

Details Interactions in noncommutative dynamics Interactions in noncommutative dynamics

1999-10-29

arxiv.org/abs/math/9910167v3

Mathematics

Operator Algebras

22 pages. Replacement corrects misnumbering of formulas in section 4. No change in mathematical content

Scientific paper

10.1007/s002200050802

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.

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