 
Summary: Noncommutative Dynamics and Esemigroups
William Arveson
Department of Mathematics, University of California, Berkeley
Email address: arveson@math.berkeley.edu
Preface
These days, the term Noncommutative Dynamics has several interpretations. It is
used in this book to refer to a set of phenomena associated with the dynamical evo
lution of quantum systems of the simplest kind that involve rigorous mathematical
structures associated with infinitely many degrees of freedom. The dynamics of
such a system is represented by a oneparameter group of automorphisms of a non
commutative algebra of observables, and we focus primarily on the most concrete
case in which that algebra consists of all bounded operators on a Hilbert space.
If one introduces a natural causal structure into such a dynamical system, then
a pair of oneparameter semigroups of endomorphisms emerges, and it is useful to
think of this pair as representing the past and future with respect to the given
causality. These are both E0semigroups, and to a great extent the problem of
understanding such causal dynamical systems reduces to the problem of under
standing E0semigroups. The nature of these connections is discussed at length in
Chapter 1. The rest of the book elaborates on what the author sees as the impor
tant aspects of what has been learned about E0semigroups during the past fifteen
