书籍介绍
《相空间中的调和分析》内容简介：The phrase "harmonic analysis in phase space" is a concise if somewhatinadequate name for the area of analysis on Rn that involves the Heisenberggroup, quantization, the Weyl operational calculus, the metaplectic representa-tion, wave packets, and related concepts: it is meant to suggest analysis on theconfiguration space Rn done by working in the phase space Rn x Rn. The ideasthat fall under this rubric have originated in several different fidds——Fourieranalysis, partial differential equations, mathematical physics, representationtheory, and number theory, among others.
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量子力学古典的函数论语言转化为李群及其表示（抽象调和分析）的框架下统一书写。量子化问题本质在相空间R2n的函数f关联一个L(Rn）算子导致坐标函数对应算子动量和坐标，函数的性质关联算子的性质。另一方面拟微分算子和其象征的关系，量子化和拟微分算子关系是一个事物的两面。Wigner-外尔变换：薛定谔图像下相空间的函数和希尔伯特空间的算子可逆关系。哈密尔顿力学是保辛形式的微分同胚。量子力学发生在射影希尔伯特空间（模常数）群表示论用在量子力学的想法 任一给定能级的本征函数被群线性变换 这些变换构成群的一个表示。辛群的基本群是Z证明利用纤维化的正合同伦序列