Interactions in Noncommutative Dynamics
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 welldefined "state of the past" and a welldefined "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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1007/s002200050802
 arXiv:
 arXiv:math/9910167
 Bibcode:
 2000CMaPh.211...63A
 Keywords:

 Mathematics  Operator Algebras
 EPrint:
 22 pages. Replacement corrects misnumbering of formulas in section 4. No change in mathematical content