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研究生： 林永康
Yung-Kang Lin
論文名稱： 幾何代數與微分形式間之轉換及其在重力之應用
Geometric Algebra and Differential Forms: Translation and Gravitational Application
指導教授： 聶斯特
James M. Nester
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
畢業學年度： 91
語文別： 英文
論文頁數： 61
中文關鍵詞： 幾何代數 、規範場論 、重力 、微分形式
外文關鍵詞： differential forms, pseudotensor, gauge theory, gravity, geometric algebra
相關次數： 點閱：10  下載：0 
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    • 幾何代數已成功應用在各物理領域, 我們希望能應用在重力上.

    Geometric Algebra already shows its power on Classical Mechanics,Electrodynamics, Quantum Mechanics and Special Relativity. It is a very handy tool for understanding and developing physics. It handles flat spacetime physics fairly well which give us the motivation to test the Gauge Theory of Gravity based on Geometric Algebra. Here we show in detail how to translate between the popular differential form approach and the Gauge Theory of Gravity-Geometric Algebra expressions. We then test on an application: the energy-momentum pseudotensor. The new formulism can handle this application well.

    1. Geometric Algebra 1.1 Introduction and Outline 1.2 From Geometry to Algebra 1.3 Even Subalgebra 1.4 Differentiation 1.5 Integration 2. Gauge Field Theory of Gravity 2.1 Local Spacetime Transformations 2.2 Metric and Einstein Equation 2.3 Equivalence Principle and Geodesic Equation 3. Translation 3.1 Connection 3.2 Torsion and Curvature Tensor 3.3 Bianchi and Contracted Bianchi Identities 3.4 Volume Elements 3.5 Einstein Tensor 4. Application and Conclusion 4.1 Einstein Pseudotensor 4.2 Dual Relation 4.3 Conclusion

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