Noncommutative Dynamics and E-Semigroups
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ISBN-13:
9780387001517
Veröffentl:
2003
Erscheinungsdatum:
12.05.2003
Seiten:
434
Autor:
William Arveson
Gewicht:
748 g
Format:
245x164x28 mm
Sprache:
Englisch
Beschreibung:
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 book introduces the notion of an E-semigroup, a generalization ofthe known concept of E-0 semigroup. These objects are families ofendomorphisms of a von Neumann Algebra satisfying certain naturalalgebraic and continuity conditions.
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.
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