Tomita-Takesaki Theory in Algebras of Unbounded Operators
Tomita-Takesaki Theory in Algebras of Unbounded Operators
复制标题
无界算子代数中的富田-竹崎理论
DOI：
10.1007/bfb0093329
复制
发表时间：
1998
影响因子：
1
通讯作者：
A. Inoue
中科院分区：
文献类型：
--
作者：
A. Inoue
这些笔记致力于系统地研究无界算子代数中von Neumann代数的Tomita-Takesaki理论的发展及其在量子物理中的应用。引入了O*-代数的标准广义向量和标准权的概念，得到了模自同构的Tomita-Takesaki理论。O~*-代数中的Tomita-Takesaki理论被应用于量子矩问题、量子统计力学和Wightman量子场论。这将是(无界)算子代数和数学物理领域的研究生和研究人员感兴趣的内容。
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.