Differential operators on von Neumann algebras

冯·诺依曼代数上的微分算子

• 批准号: 0070634
• 负责人: Nikolai Weaver
• 金额: $ 9.6万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070634&HistoricalAwards=false
• 关键词: Differential; operators; von; Neumann; algebras

Differential operators on von Neumann algebrasNikolai WeaverProject SummaryDifferential operators on operator algebras have been studiedextensively as a model for the infinitesimal time developmentof a quantum-mechanical system, either isolated or interactingwith a macroscopic system. The proposed research involves astudy of differential operators on von Neumann algebras buildingon the investigator's prior work on the special case of first-orderdifferential operators.Operators on a Hilbert space are infinite analogs of finitematrices. They have applications throughout mathematics, butthe proposed research relates specifically to mathematicalphysics. Von Neumann algebras of operators have been used to modelcertain quantum mechanical systems, particularly those arising inquantum statistical mechanics. The proposal involves using ideasof Fields medalist Alain Connes to study the time-evolution ofthese algebras, with the double aim of clarifying the generaltheory and giving insight into specific examples.

von Neumann代数上的微分算子作为量子力学系统无限小时间发展的模型被广泛研究，无论是孤立的还是与宏观系统相互作用的。在研究者先前关于一阶微分算子的特殊情况的工作的基础上，提出了关于von Neumann代数上的微分算子的研究。希尔伯特空间上的算子是有限矩阵的无限类似物。它们在整个数学中都有应用，但拟议的研究特别涉及数学物理。冯·诺伊曼算子代数已被用于模拟某些量子力学系统，特别是那些产生量子统计力学的系统。该提案涉及使用菲尔兹奖获得者阿兰·科恩斯的思想来研究这些代数的时间演化，其双重目的是阐明一般理论并深入了解具体的例子。