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Noncommutative Dynamics and E-Semigroups

Noncommutative Dynamics and E-Semigroups
Catalogue Information
Field name Details
Dewey Class 515.724
Title Noncommutative Dynamics and E-Semigroups ([EBook] /) / by William Arveson.
Author Arveson, William
Other name(s) SpringerLink (Online service)
Publication New York, NY : : Springer New York : : Imprint: Springer, , 2003.
Physical Details X, 434 p. : online resource.
Series Springer monographs in mathematics 1439-7382
ISBN 9780387215242
Summary Note The term Noncommutative Dynamics can be interpreted in several ways. It is used in this book to refer to a set of phenomena associated with the dynamics 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 noncommutative algebra of observables, and the author focuses primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space. This subject overlaps with several mathematical areas of current interest, including quantum field theory, the dynamics of open quantum systems, noncommutative geometry, and both classical and noncommutative probability theory. This is the first book to give a systematic presentation of progress during the past fifteen years on the classification of E-semigroups up to cocycle conjugacy. There are many new results that cannot be found in the existing literature, as well as significant reformulations and simplifications of the theory as it exists today. William Arveson is Professor of Mathematics at the University of California, Berkeley. He has published two previous books with Springer-Verlag, An Invitation to C*-algebras (1976) and A Short Course on Spectral Theory (2001).:
Contents note 1. Dynamical Origins -- 1.1. The Flow of Time in Quantum Theory -- 1.2. Causality and Interactions -- 1.3. Semigroups of Endomorphisms -- 1.4. Existence of Dynamics -- 1. Index and Perturbation Theory -- 2. E-Semigroups -- 3. Continuous Tensor Products -- 4. Spectral C*-Algebras -- 2. Classification: Type I Cases -- 5. Path Spaces -- 6. Decomposable Product Systems -- 3. Noncommutative Laplacians -- 7. CP-Semigroups -- 8. C*-Generators and Dilation Theory -- 9. Index Theory for CP-Semigroups -- 10. Bounded Generators -- 4. Causality and Dynamics -- 11. Pure Perturbations of CAR/CCR Flows -- 12. Interaction Theory -- 5. Type III Examples -- 13. Powers’ Examples -- 14. Tsirelson-Vershik Product Systems.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-0-387-21524-2
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