an:00053348
Zbl 0749.46038
Baumg??rtel, Hellmut; Wollenberg, Manfred
Causal nets of operator algebras. Mathematical aspects of algebraic quantum field theory
EN
Mathematische Lehrb??cher und Monographien. II. Abteilung: Mathematische Monographien. 80. Berlin: Akademie Verlag. xviii, 460 p. (1992).
00454355
1992
b
46L60 46Lxx 46N50 46-02 81T05 82B10
decomposition theory; Quantum field theory; Algebraic statistical mechanics; nets of \(C^*\)-algebras and von Neumann algebras; quasi-local algebras; net automorphisms; causality; cluster properties; CAR and CCR algebras; modular theory; nuclearity; superselection theory; representations; intertwiners; endomorphisms; Hilbert \(C^*\)-systems; inverse superselection theory
This book meets the request of people working in Mathematical Physics, at least those who are concerned with functional-analytic methods.
Part I (Fundamentals of operator algebras, \(C^*\)-algebras, von Neumann algebras, decomposition theory) provides basic material that is presumably widely known; thus it is more or less to be regarded as an introduction.
Part II as well as Part IV are related to Quantum field theory and Algebraic statistical mechanics ( nets of \(C^*\)-algebras and von Neumann algebras, quasi-local algebras, net automorphisms, causality, cluster properties, CAR and CCR algebras).
Part V deals with modular theory and (local) type III, or III-1, algebras, and nuclearity.
Part III yields a very elaborate presentation of superselection theory ( representations, intertwiners, endomorphisms), Hilbert \(C^*\)-systems, inverse superselection theory, Mackey theory.
All in all, this is a very comprehensive book.
A.Wehrl (Wien)