数学. 笔记 [notes]

    以下是蒋济仁的数学相关笔记合集:

    The following is a collection of Jiang Jiren’s mathematics-related notes:

    讨论班讲义: / Seminar Notes:

    • 量子规范理论的数学方法讨论班讲义1: [PDF]

      为我与冯梓轩于2024年关于鬼场与BRST量子化的系列讨论成果. 讨论内容主要来自 Henneaux 与 Teitelboim 的书籍 “Quantization of Gauge systems”.

      A series of discussions in 2024 between myself and Feng Zixuan on ghost fields and BRST quantization. The discussions were primarily based on the book “Quantization of Gauge systems” by Henneaux and Teitelboim.

      该讲义叙述了书籍中规范系统的定义, 以 BRST量子化 处理规范系统的方法 (包括引入鬼场) 以及此类系统的 哈密顿-拉格朗日 对偶 (正则量子化-路径积分量子化的对应) , 试图借助数学直观为BRST鬼场量子化理论给出一个形象化, 直觉化的解释.

      These notes describe the definition of gauge systems from the book, the method of BRST quantization for handling gauge systems (including the introduction of ghost fields), and the Hamiltonian-Lagrangian duality for such systems (the correspondence between canonical quantization and path integral quantization). It attempts to provide a visual and intuitive mathematical explanation for the BRST ghost field quantization theory.

      特此向在讨论中做出主要贡献的冯梓轩同学表示感谢.

      Special thanks to Feng Zixuan for his major contributions to the discussions.

    • 量子规范理论的数学方法讨论班讲义2: [PDF]

      这是一个极为粗糙的手写讲义, 内容较为破碎, 记录了我与冯梓轩, 向昕宇, 刘九和, 丁徐祉晗等同学进行后续讨论的内容. 内容包括CFT, 协变相空间, BV量子化等.

      This is a very rough, handwritten set of notes with fragmented content. It records follow-up discussions with fellow students Feng Zixuan, Xiang Xinyu, Liu Jiuhe, Ding Xuzhihan, and others. Topics include CFT, covariant phase space, BV quantization, etc.

      讲义本人暂无分享学习价值, 但有计划转写为LaTeX文档.

      The notes in their current form have little learning value for sharing but there are plans to transcribe them into LaTeX.

    课程讲义: / Course Notes:

    • Dimer Model 课程讲义 (英文): [PDF]

      为清华大学2024-2025秋季学期由 Nicolai Reshetikhin 教授的数学物理课程准备的课程讲义, 由我基于授课教师的手写笔记转写为LaTeX文档.

      Course notes prepared for the Mathematical Physics class taught by Professor Nicolai Reshetikhin in the Fall 2024-2025 semester at Tsinghua University. I transcribed these into LaTeX based on the instructor’s handwritten notes.

      讲义本身目前错误较多, 且来不及一一矫正, 仅供参考使用.

      The notes currently contain many errors and there has been no time to correct them one by one. They are for reference only.

    部分课程笔记: / Other Course Notes:

    敬请期待 / More to come.