Operator Algebras and Quantum Statistical Mechanics 1

C*- and W*-Algebras. Symmetry Groups. Decomposition of States

Ola Bratteli, Derek William Robinson (Autoren)

Buch | Hardcover

XIV, 506 Seiten

1987 | 2nd ed. 1987
Springer Berlin (Verlag)
978-3-540-17093-8 (ISBN)

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In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

1. Introduction.- 2. C-Algebras and von Neumann Algebras: C-Algebras; Representations and States; von Neumann Algebras; Tomita--Takesaki Modular Theory and Standard Forms of von Neumann Algebras; Quasi-Local Algebras; Miscellaneous Results and Structure.- 3. Groups, Semigroups, and Generators: Banach Space Theory; Algebraic Theory.- 4. Decomposition Theory: General Theory; Extremal, Central, and Subcentral Decompositions; Invariant States; Spatial Decomposition.- References.- List of Symbols.- Subject Index.

Erscheint lt. Verlag	27.5.1987
Reihe/Serie	Theoretical and Mathematical Physics
Zusatzinfo	XIV, 506 p.
Verlagsort	Berlin
Sprache	englisch
Maße	156 x 234 mm
Gewicht	895 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Technik
Schlagworte	Algebra • Algebras • Mechanics • Operator • Operator algebra • Operatoralgebra • operator theory • Physics • Physik • Quantenmechanik • Quantenstatistik • Statistische Mechanik
ISBN-10	3-540-17093-6 / 3540170936
ISBN-13	978-3-540-17093-8 / 9783540170938
Zustand	Neuware