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Noncommutative Dynamics and E-semigroups William Arveson

Summary: Noncommutative Dynamics and E-semigroups
William Arveson
Department of Mathematics, University of California, Berkeley
E-mail address: arveson@math.berkeley.edu
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 one-parameter 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 one-parameter 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 E0-semigroups, and to a great extent the problem of
understanding such causal dynamical systems reduces to the problem of under-
standing E0-semigroups. 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 E0-semigroups during the past fifteen


Source: Arveson, William - Department of Mathematics, University of California at Berkeley


Collections: Mathematics