Aspects of Non-Commutative Dynamics: Powers’ Problems and its Solution

Abstract : Dynamics of a quantum system is represented by E0-semigroups on some algebra of non-commuative observables such as B(H). E0-semigroups are semigroup of unital normal ∗-endomorphisms α = (αt)t≥0 with point-wise weak* continuous in time parameter. Classification of E0-semigroups upto cocycle conjugacy is a major task in non-commuative dynamics. E0-emigroups are uniquely determined by their product systems. In this context, I will discuss a problem raised by Powers and its solution and further developments.