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.Comment: 22 pages. Replacement corrects misnumbering of formulas in section 4.
No change in mathematical conten