“量化是个谜”
"Quantization is a mystery"
摘要：
结合量子物理学发展的历史调查和量子理论中选定的数学主题的回顾的注释（针对量子力学不完全新手的学生）。在引言中回顾了量子革命的早期阶段，并在第2.1节中概括了辛几何的一些基本概念之后，我们在第2.2节中考察了所谓的预量子化，从而为几何量子化的概述（第2.3节）奠定了基础。在第三节中，我们应用一般理论研究凯勒流形量子化的基本例子。在第四节中，我们回顾了Weyl和Wigner映射以及Groenewold和Moyal的工作，它们奠定了相空间中量子力学的基础，最后简要回顾了形变量子化的现代发展。第5节提供了对二次量子化及其数学解释的回顾。我们指出，（非相对论）束缚态的治疗需要超越整洁的数学形式化的概念的二次量子化。附录专门介绍帕斯夸尔·乔丹，他是量子力学的创造者中最不为人所知的人，也是“量子化物质波理论“的总设计师。
英文摘要：
Expository notes which combine a historical survey of the development of quantum physics with a review of selected mathematical topics in quantization theory (addressed to students that are not complete novices in quantum mechanics). After recalling in the introduction the early stages of the quantum revolution, and recapitulating in Sect. 2.1 some basic notions of symplectic geometry, we survey in Sect. 2.2 the so called prequantization thus preparing the ground for an outline of geometric quantization (Sect. 2.3). In Sect. 3 we apply the general theory to the study of basic examples of quantization of Kaehler manifolds. In Sect. 4 we review the Weyl and Wigner maps and the work of Groenewold and Moyal that laid the foundations of quantum mechanics in phase space, ending with a brief survey of the modern development of deformation quantization. Sect. 5 provides a review of second quantization and its mathematical interpretation. We point out that the treatment of (nonrelativistic) bound states requires going beyond the neat mathematical formalization of the concept of second quantization. An appendix is devoted to Pascual Jordan, the least known among the creators of quantum mechanics and the chief architect of the "theory of quantized matter waves".
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