我們在這篇論文裡主要是介紹旋量(Spinor)，以及運用對稱性去分析其性質，與推算出旋量在旋量空間下的特性。內文中我們試著用推算出的旋量方程式去描述電磁場，並且以旋量的結果去對照張量所算出的結果。最後我們試著分析重力場的旋量表示式，並且定義Weyl Spinor，藉著Schwarzschild solution 的例子去探討它在旋量中的表示式以及試著去分類它。

This thesis is an introduction to the 2-spinor formalism. First we discuss the spinor algebra, and derive some important properties of the spinor space. Then, we consider some physical fields, and try to translate them into spinor form. In there, we choose the electromagnetic field, with classification in both the tensor and the spinor forms. After that we study the Weyl spinor and work out the algebraic type of the Schwarzschild solution.

Chapter 1 Introduction                                    1

Chapter 2 Spinor algebra
2.1 Spinor space                                          3
2.2 Levi-Civita spinor                                    5
2.3 spinor symmetry operations                            11

Chapter3 Electromagnetic Tensor
3.1 Classification of the electromagnetic tensor          13
3.2 Electromagnetic spinor and its classification         17

Chapter 4 Weyl Tensor
4.1 Curvature spinor                                      26
4.2 Classification of the Weyl spinor                     29
4.3 Algebraic type of the Schwarzschild Weyl spinor       33

Chapter 5 Conclusions                                     36
Reference                                                 37

[1] Hing-Tong Cho, Lecture notes on Special and General Relativity
[2] Peter O’Donnell, “Introduction to 2-spinors in General Relativity”, (World Scientific Publishing 2003)
[3] Gerardo F. Torres del Castillo, “Spinors in Four-Dimensional Spaces”, Progress in Mathematical Physics, Vol 59 (2010)
[4] Mikio Nakahara, “Geometry, Topology and Physics”, (Institute of Physics Publishing 2003)