Contractive Projections, Quantum Mechanics and Operator Spaces

收缩投影、量子力学和算子空间

• 批准号: 0101153
• 负责人: Bernard Russo
• 金额: $ 7.24万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0101153&HistoricalAwards=false
• 关键词: Contractive; Projections; Quantum; Mechanics; Operator

This research plan consists of two themes. The first is concernedwith investigations into the structure theory of injective-like objects inthe category of operator spaces, and involves the theory ofcontractive projections on real or complex C*-algebras. The second isa study of linear and nonlinear representations of the Lorentz group withan eye towards finding physically meaningful models in mathematicalphysics. The link connecting these two objectives is described in thefollowing paragraph.Since the pioneering work of Jordan, von Neumann and Wigner in the 1930s,Segal in the 1940s and 50s, and Alfsen-Shultz-Stormer in the 1970s, Jordanalgebras, and more recently Jordan triples, have been used as a model forthe study of the state spaces of quantum mechanics. On the other hand,contractive projections have played a key role in the structure theory ofBanach Jordan triple systems, and those which are completely contractivegive rise to injectives in the category of operator spaces (also known asquantized Banach spaces). The PIs plan to study the fine structure ofcontractive projections on operator spaces in order to gain a betterunderstanding of their role in operator space theory, as well as theirrole, together with Jordan structures, in quantum mechanics andrelativity.

本研究计划包括两个主题。第一部分研究了算子空间范畴内类注入对象的结构理论，包括实或复C*-代数上的压缩投影理论。二是研究洛伦兹群的线性和非线性表示，以期在数学物理中找到有物理意义的模型。下面一段将说明这两个目标之间的联系。自从Jordan、von Neumann和Wigner在20世纪30年代，Segal在20世纪40年代和50年代，Alfsen-Shultz-Stormer在20世纪70年代的开创性工作以来，Jordanalgebras，以及最近的Jordan三元组，已经被用作量子力学状态空间研究的模型。另一方面，压缩投影在Banach Jordan三重系统的结构理论中发挥了关键作用，那些完全压缩的投影在算子空间（也称为量子化的Banach空间）的范畴中产生了注入。pi计划研究算子空间上的收缩投影的精细结构，以便更好地理解它们在算子空间理论中的作用，以及它们与约旦结构在量子力学和相对论中的作用。