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研究生：	陳佳宜
論文名稱：	德西特空間粒子對創生 Particle pair creation in the de Sitter space
指導教授：	高賢忠
學位類別：	碩士 Master
系所名稱：	物理學系 Department of Physics
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	61
中文關鍵詞：	德西特空間、克萊茵-高登方程、狄拉克方程、真空態
英文關鍵詞：	de Sitter space, Klein-Gordon equation, Dirac equation, vacuum states
論文種類：	學術論文
相關次數：	點閱：105 下載：23
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本文介紹德西特空間的特性，並在其三個最常見的時空坐標，即球坐標系、龐加萊坐標系、全域坐標系，求出對應之克萊茵-高登方程式、狄拉克方程式的解。這些純量場及費米子場的解可以用來建構創生與消滅算符、定義真空態，並研究真空粒子對產生與湮滅的過程。

In this thesis, we derive the exact solutions to the Klein-Gordon equations and the Dirac equations for the three coordinate systems in the de Sitter space: the spherical coordinate system, the Poincaré coordinate system, and the global coordinate system.
By choosing proper boundary conditions of the system, we construct the in-vacuum and out-vacuum states which can be used to study the process involving creation and annihilation of particle and anti-particle pairs.

中文摘要    I
Abstract    II
Contents    1
Chapter 1 Introduction    3
Chapter 2 General Relativity    5
2.1 Notations    5
2.2 Basic concepts    6
2.3 General coordinate basis and local Lorentz frame    8
2.4 Covariant derivative and connections    10
2.5 The de Sitter Space    12
2.5.1 The spherical coordinate system    12
2.5.2 The Poincaré coordinate system    13
2.5.3 The global coordinate system    14
2.6 The Einstein-field equations    16
Chapter 3 Scalar field in the de Sitter space    17
3.1 The Klein-Gordon equation in general relativity    17
3.2 Scalar field in the spherical coordinates    20
3.3 Scalar field in the Poincaré coordinates    24
3.4 Scalar field in the global coordinates    26
Chapter 4 Spinor field in the de Sitter space    31
4.1 The Dirac equation    31
4.2 Spinor field in the spherical coordinates    36
4.3 Spinor field in the Poincaré coordinates    45
4.4 Spinor field in the global coordinates    48
Chapter 5 Conclusion    55
Reference    57

                                

[1] N. D. Birrell and P. C. W. Davies. Quantum fields in curved space. (1982) Cambridge University Press.
[2] “De Sitter universe.” http://en.wikipedia.org/wiki/De_Sitter_universe. 25 Aug 2013.
[3] Steven Weinberg. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. (1972) John Wiley & Sons, Inc. New York London Sydney Toronto.
[4] Michael T. Vaughn. Introduction to Mathematical Physics (2007) Wiley.
[5] Andrew J. S. Hamilton. “General Relativity, Black Holes, and Cosmology.” Center for Astrophysics and Space Astronomy, University of Colorado.
[6] Jeffrey Yepez. “Einstein’s Vierbein Field Theory of Curved Space.” arXiv:1106.2037v1 [gr-qc] 10 Jun 2011.
[7] Lewish H. Ryder. Quantum Field Theory. (1996) Cambridge University Press.
[8] Syed Alwi B. Ahmad. “Fermion Quantum Field Theory In Black-hole Spacetimes.” 18 April 1997.
[9] J.J. Sakurai. Advanced Quantum Mechanics. p.124-p.125 (1967) Addison-Wesley Publishing Company.
[10] Ion I. Cotǎescu. “The Dirac particle on de Sitter background.” (1998) Mod. Phys. Lett. A 13, 2991-2998. DOI:10.1142/S021773239800317X.
[11] R. Brout and S. Massar, 15 July 1995. “Quantum source of the back reaction on a classical field.” PHYSICAL REVIEW D. Vol. 52, No. 2.
[12] P. C. W. Davies, Sep 2001. “Quantum vacuum noise on physics and cosmology.” CHAOS, Vol. 11, No. 3.

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