Tomita-Takesaki theory in algebras of unbounded operators
By: Atsushi Inoue.
Series: Lecture notes in mathematics,; 1699; Lecture notes in mathematics (Springer-Verlag) ;; 1699.
Publisher: Springer
Published: 1998
Place of publication: Berlin; New York
Language: eng
Number of pages: 241
Subjects: Von Neumann algebras; Quantum theory; Operator algebras
Description: These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.
Notes: Includes bibliographical references (p. [225]-238) and index.