Spin Geometry   [Hydrogen Atom]

第一章 Clifford Algebra

  1. Introduction       A child guide to spinors   Differential operators
  2. Clifford product (Reflection and Rotation: (1) Infinitesimal Generators)
  3. Clifford algebra   [cl3]  [Spin(3)]   [旋轉(Clifford group)]   [cl4 and Spin(4)]    習作   習作

第二章  Lorentz Group

  1. [Lorentz Transformation]  The Lorentz Group and Lorentz spin group   SO(4)     [SO(3)]  [SU(2)]   習作
  2. Represetations of the Lorentz Groups  SL(2,C)  [表示隨處可見(席南華)]   [Topics in Representation Theory by (Giovanni Russo)]
  3. SO(3)   [Irreducible Representation]   [Spherical Harmonics]

第三章  Spinors

  1. 立體投影將球面上的點和酉旋量聯繫起來  (2) 建構一個酉旋量  (3)The Pauli matrices  (4) Hermitian Vector Spaces
  2. Pauli Spinors    [Energy mass equation]  [Klein-Gordon equation]  [Dirac equation如何開根號 (Dirac spinor)]  [自旋電子]
  3. Spin Structure    Spinor Bundle   The Spin manifolds
  4.  [Spinor representations]

第四章  Dirac Operator

  1. The classical Dirac operator on spinors    [Dirac operator(1)]    [Dirac Operator(2)]   [The Dirac spectrum S^3的Dirac譜]
  2. Electromagnetic Field(電磁場與Dirac current J(x)]
  3. Connections and Curvature
  4. Twisted Dirac Operator and Index Theory

第五章  

  1. 薛丁格方程
  2. Spinors in 4-dimensional spaces   Gerardo F.Torres del Castillo(墨西哥)
    1.Spinor Algebra  2.Conection and Curveture  3.Applications to GR  4.Further Aplications
    Killing Spinors   [Exercise 1] [Exercise 2] [Exercise 3] [Exercise 4]
  3. The Dirac equation in Curved Spacetime   Peter Collas and David Klein
  4. The heat equation and index theory(熱核理論)   Atiyah-Singer-Index theorem  [Michael Atiyah and Isadore Singer]
  5. 正標量曲率(positive scalar curvature) : 一個給定的流形上是否存在一個具有正標量曲率的黎曼度量？ Gromov-Lawson-Rosenberg conjecture [Open Problems]
  6. Kahler Manifolds and Complex Dirac Operators
  7. The Seiberg-Witten and Twistor Construtions(或Weitzenbock 公式應用)
  8. Applications to Gauge Theory and Topology
  1. A Child Guide to Spinors      William O. Straub
  2. [Clifford Algebra and Spinors]  by Pertti Lounesto  習作
  3. [An Introduction Theory of Spinors]  by Moshe Carmeli   Shimon Malin   習作
  4. [Spinors in Physics]  by Jean Hladik  習作 (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)
  5. [An Introduction to Clifford Algebras and Spinors]   by Jayme Vaz and Roldao da Rocha   習作
  6. [Spin Geometry] by  Christian Bar
  7. [Spinors in Four-Dimensional Spaces]  by    習作
  8. [Spinors and Space-time]  by  R.Penrose and W.Rindler
  9. [Clifford Algebra]  by Daniel Klawitter
  10. [Lecture Notes on Spin Geometry]  by Konstantin Wernli
  11. 張海潮先生的 (1)狹義相對論 (2)曲率公式 (3)伽利略與勞倫茲變換 (4)勞倫茲變換推導 (5)Minkowski metric  如何解愛因斯坦方程式
  12. George Uhlenbeck 1925       電子自旋