Histories Distorted by Partial Isometries

In quantum dynamical systems, a history is defined by a pair (M,\γ), of a type I factor M, acting on a Hilbert space H, and an₀-group \γ = (\γₜ)_t\∈ , satisfying certain additional. In this paper, we distort a given history (M,\γ), by a finite of partial isometries on H. In particular, such a is dictated by the combinatorial relation on the family. Two main purposes of this paper are (i) to show the existence of on histories, and (ii) to consider how distortions work. We can Sections 3, 4 and 5 as the proof of the of distortions (i), and the properties of distortions (ii) are shown Section 6.