Operator Algebras In Dynamical Systems (encyclopedia Of Mathematics And Its Applications)
by Shtichirt Sakai /
1991 / English / PDF
4.8 MB Download
This book is concerned with the theory of unbounded derivations in
C*-algebras, a subject whose study was motivated by questions in
quantum physics and statistical mechanics, and to which the author
has made considerable contributions. This is an active area of
research, and one of the most ambitious aims of the theory is to
develop quantum statistical mechanics within the framework of
C*-theory. The presentation concentrates on topics involving
quantum statistical mechanics and differentiations on manifolds.
One of the goals is to formulate the absence theorem of phase
transitions in its most general form within the C* setting. For the
first time, the author globally constructs, within that setting,
derivations for a fairly wide class of interacting models, and
presents a new axiomatic treatment of the construction of time
evolutions and KMS states.
This book is concerned with the theory of unbounded derivations in
C*-algebras, a subject whose study was motivated by questions in
quantum physics and statistical mechanics, and to which the author
has made considerable contributions. This is an active area of
research, and one of the most ambitious aims of the theory is to
develop quantum statistical mechanics within the framework of
C*-theory. The presentation concentrates on topics involving
quantum statistical mechanics and differentiations on manifolds.
One of the goals is to formulate the absence theorem of phase
transitions in its most general form within the C* setting. For the
first time, the author globally constructs, within that setting,
derivations for a fairly wide class of interacting models, and
presents a new axiomatic treatment of the construction of time
evolutions and KMS states.
