$\textbf{1.平方型拉氏量}$

$$L=a(t){\dot q}^2+b(t)q\dot q+c(t)q^2+d(t)\dot q+e(t)q+f(t)$$

体系的积分路径$q(t)$可视为是经典路径$q_{cl}(t)$扰动而变形后的路径。
经典路径满足欧拉－拉格朗日方程$\dfrac{d}{dt} \dfrac{\partial L}{\partial \dot q}-\dfrac{\partial L}{\partial q} = 0$。

用$x(t)$表示相对 $q_{cl}(t)$的扰动，则体系的路径可表示为：

\begin{align}
q(t)&=q_{cl}(t)+x(t)&\
\dot q(t)&=\dot q_{cl}(t)+\dot x(t)&
\end{align}

凝聚态物理

• Lectures on Condensed Matter – Anushya Chandran, Roger Melko, Xiao-Gang Wen

• Condensed Matter – from 2010

• Condensed Matter Physics and Topological Field Theory

• UIUC Joint Workshop on Strongly Correlated Quantum Many-Body Systems 2015

• Condensed Matter Review (PHYS 637) – Xiao-Gang Wen

• Quantum criticality and High-$T_c$ superconductivity – K. Efetov

• The Physics of Superconducting Devices - Anthony Leggett

量子场论

• QFT part I – Dan Wohns, PSI 17/18

• QFT part II – Francois David, PSI 17/18

• QFT part III – Jaume Gomis, PSI 17/18

• Advanced QFT: the theory of elementary interactions – Hannover

• 北京大学 二维共形量子场论的数学化以及在数学中的应用

• Introduction to Conformal Field Theory – Hannover

量子群

• Introduction to Quantum Groups

• Quantum Groups – Moritz Weber

• Quantum Groups and 3-Manifold Invariants

• Quantum Groups and Quantum Cohomology – Andrei Okounkov

微分几何与广义相对论

• Geometric Anatomy of Theoretical Physics – Fredric Schuller

• Symplectic geometry and Classical Mechanics – Hannover

• 北京师范大学 赵峥 广义相对论基础

• 北京师范大学 梁灿彬 微分几何与广义相对论教程

• 北京师范大学 梁灿彬 李群李代数与纤维从及其在规范场论中的应用

• 北京师范大学 周彬 李代数理论及其在物理学中的应用

• 广义相对论与引力：从数学背景到物理图景

• On the Mathematical Theory of Black Holes – Sergiu Klainerman

• Quantum Fields, Strings and Black Holes – Atish Dabholkar

• Asymptotic symmetries, black holes, and holography

代数几何

• Algebraic Topology – Chen-Yu Chi

• Algebraic Topology – Fernando Rodriguez Villegas

• Algebraic Geometry – Lothar Gottsche

• Algebraic Geometry – Waterloo】

• Algebraic Geometry for Physicists – Ugo Bruzzo

• Complex Geometry – Chen-Yu Chi

• Noncommutative Projective Geometry – Dan Rogalski

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