Tomita-Takesaki Theory in Algebras of Unbounded Operators [electronic resource] / by Atsushi Inoue.

By:

Inoue, Atsushi [author.]

Contributor(s):

SpringerLink (Online service)

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 1699Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998Description: VIII, 244 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540494959

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

512 23

LOC classification:

QA150-272

Online resources:

Click here to access online

Contents:

Fundamentals of O*-algebras -- Standard systems and modular systems -- Standard weights on O*-algebras -- Physical applications.

In: Springer eBooksSummary: 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.

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Fundamentals of O*-algebras -- Standard systems and modular systems -- Standard weights on O*-algebras -- Physical applications.

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.

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