A bounded operator approach to Tomita-Takesaki theory
نویسندگان
چکیده
منابع مشابه
Tomita-takesaki Theory
Definition 1.1. Let A be an involutive algebra over C with involution ξ 7→ ξ (resp. ξ 7→ ξ). We say A is a left (resp. right) Hilbert algebra if A has a inner product (· | ·) satisfying: a. Multiplication on the left (resp. right) is a bounded operator; that is, ∀ξ ∈ A the map πl(ξ) : η 7→ ξη (resp. πr(ξ) : η 7→ ηξ) is bounded on A. b. (ξη | ζ) = (η | ξζ) (resp. (ξη | ζ) = (ξ | ζη)). c. The inv...
متن کاملTomita–Takesaki Modular Theory
We provide an brief overview of Tomita–Takesaki modular theory and some of its applications to mathematical physics. This is an article commissioned by the Encyclopedia of Mathematical Physics, edited by J.-P. Francoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house.
متن کاملClassical KMS Condition and Tomita-Takesaki Theory
Relationships between the classical KMS condition and the time evolution for classical systems are discussed.
متن کاملBoundary conformal fields and Tomita–Takesaki theory
Motivated by formal similarities between the continuum limit of the Ising model and the Unruh effect, this paper connects the notion of an Ishibashi state in boundary conformal field theory with the Tomita–Takesaki theory for operator algebras. A geometrical approach to the definition of Ishibashi states is presented, and it is shown that, when normalisable the Ishibashi states are cyclic separ...
متن کاملApplication of Tomita-Takesaki theory in algebraic euclidean field theories
The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one should be able to extract information about the behavior of the correlation functions of the Minkowskian counterpart. We think that the C*-algebraic approach to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1977
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1977.69.187