Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics (North-Holland Mathematics Studies)

书籍介绍(英文)

Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas. This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C * -algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra. Also examined are C * -algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A.


从历史上看，算子理论和代表性的理论既与量子力学的出现起源。学科之间的相互作用，一直并且仍然在各个领域的活跃。这一卷的重点是普遍包络代数陈述，陈述变一般，和无限的，特别是维李代数。它还提供了对有限维李代数积最新成果的新应用。作为一个中心主题，这是表明，在算子代数的一些事态发展可能会处理特别优雅的方式由李代数，扩展使用和投影意见。在一些情况下，李代数方法在数学物理问题*和C -代数理论是新的，例如，李的弯曲磁场汉密尔顿谱理论代数治疗，不合理的旋转式代数治疗，以及Virasoro代数。还审查是C *代数使用的方法（在非传统的方式）在无穷维李代数及其扩展交涉研究，由A.孔涅和发展的方法马