经典力学与量子力学的李代数
Classical and Quantum Mechanics via Lie algebras
摘要：
这本书的目标是目前的经典力学，量子力学，统计力学在一个几乎完全代数设置，从而介绍数学家，物理学家和工程师的想法有关的经典和量子力学与李代数和李群。这本书强调了经典力学和量子力学的接近性，材料的选择方式是使这种接近性尽可能明显。这里涉及的大部分材料都不是经典或量子力学标准教科书处理的一部分（或者只是在那里进行了表面处理）。对于物理学学生谁想要得到一个更广泛的看法的主题，这本书可能因此作为一个有用的补充，标准治疗的量子力学。几乎无一例外，这本书是关于经典力学，量子力学和统计力学中的精确概念和精确结果。力学的结构性质的讨论独立的计算技术，从所作的假设获得定量正确的数字。用于从第一原理计算材料的显式热力学性质或高能实验的显式截面的标准近似机械可以在许多教科书中找到，这里不再重复。
英文摘要：
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
