旋  量

  1. A Child Guide to Spinors      William O. Straub   [Spin Geometry的前沿]
  2. George Uhlenbeck 1925       電子自旋      [Hydrogen Atom]

 [Spin Geometry] by  Christian Bar      [Spinors in Physics]  by Jean Hladik

Differential operator on manifolds

  1. Introduction       A child guide to spinors
  2. Differential operators
  3. Sobolev spaces
  4. Laplace-type and Dirac-type operators
  5. Hodge theory

Spinors and the classical Dirac operator

  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   (5) 習作
  2. Rotation: (1) Infinitesimal Generators   [習作]
  3. SO(3)   [Irreducible Representation]   [Spherical Harmonics]   [Spinor representations]   [習作]
  4. Pauli Spinors    [Energy mass equation]  [Klein-Gordon equation]  [Dirac equation如何開根號 (Dirac spinor)]  [自旋電子]
  5. 薛丁格方程     [習作]
  6. The Lorentz Group   SO(4)   [Lorentz Transformation]  [習作]
  7. Represetations of the Lorentz Groups  SL(2,C) [習作]
  8. Dirac Spinors   [習作]
  9. Clifford algebra   [cl3]  [Spin(3)]   [旋轉(Clifford group)]   [cl4]   習作   習作   [習作]
  10. The Spin group
  11. The classical Dirac operator on spinors    [Dirac operator]    [The Dirac spectrum]  [S^3的Dirac譜]
  12. Hypersurfaces]

Electromagnetism(電磁場)

  1. Lorentz transformations

The heat equation and index theory

  1. The heat kernel
  2. The formal heat kernel
  3. McKean-Singer formula
  4. Asymptotic of the heat kernel
  5. Growth of eigenvalues
  6. The index of Dirac-type operators      Dirac譜  [何謂Spinor Bundle]

Characteristic Classes

  1. Chern Classes
  2. Additive and multiplicative classes
  3. Pontryagin Classes

Index theorems for Dirac -type operators

  1. Atiyah-Singer Index theorem
  2. Hirzebruch signature theorem

Semi-Riemannian Spin Geometry

  1. The Spin Group      Minkowski空間的自旋變換群
  2. Spinors             Spin manifold
  3. Spin structure   Spin structure(S^3)
  4. Spin connections
  5. The classical Dirac operator on spinors
  6. Spacelike hypersurface of Lirentzian manifolds

An Introduction Theory of Spinors      Moshe Carmeli   Shimon Malin

第一章 Group Theory                                [SO(3)]  [SU(2)]

第二章 Representation Theory

第三章 The Lorentz and SL(2,C) Groups

第四章 Two-component Spinors

第五章 Maxwell,Dirac and Pauli Spinors

  1. Maxwell equations
  2. Spinors in curved Spacetime
  3. Covariant Derivative of a Spinor
  4. The Electromagnetic Field Spinors
  5. Problems

第六章 The Gravitational Field Spinors

第七章 The Gauge Field Spinors

第八章 The Euclidean Gauge Field Spinors