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研究生:黃柏傑
研究生(外文):Bo-Jie Huang
論文名稱:在非交換規範場中的膺能隙形成機制
論文名稱(外文):Pseudogap Formation in Non-abelian Gauge System
指導教授:陳智泓陳智泓引用關係
指導教授(外文):Chyh-Hong Chern
口試委員:賀培銘胡崇德
口試委員(外文):Pei-Ming HoChong-Der Hu
口試日期:2015-07-30
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:36
中文關鍵詞:膺能隙非交換規範場超導體
外文關鍵詞:PseudogapNon-abelianGauge SystemSuperconductor
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在⾼高溫超導中,許多的特性並不同於⼀一般超導體,尤其是在銅氧化物在尚未 進⼊入超導相時便出現了膺能隙,這個問題困擾著凝態物理學家⾧長達 30 年,近來隨 著鐵基超導體、︑﹑重費⽶米⼦子超導體的誕⽣生也發現有膺能隙的⽣生成,於是物理學家們 便希望對這種特性有⼀一個統⼀一的解釋。︒。
2014 年,陳智泓教授利⽤用 U(1)規範場在反鐵磁場擾動中獲得質量,希望能解 釋膺能隙的產⽣生,⽽而本⽂文希望能將適⽤用範圍擴⼤大到 SU(2)及更⾼高的對稱性,⽽而進⼀一 步解釋在擁有多重能帶超導體中膺能隙的形成機制。︒。

There are many special and novel characteristics in high Tc superconductors which do not show in conventional superconductors. One of most peculiar features is the pseudogap. It confuses physicist that why the cuprates go into a gap phase which doesn’t show superconductivity. Recently, many materials are discovered and showing unconventional superconductivity, such as Iron pnictide superconductors and heavy fermion superconductors, which also perform the pseudogap feature. It drives physicist to find out the relation between those materials.
In 2014, Prof. Chern considered the pseudogap may be explained by a U(1) gauge field acquiring mass from a Stuckelberg field, which comes from antiferromagnetic fluctuation. In this thesis, I will generalize the abelian system to the non-abelian systems such as SU(2) systems or higher symmetry systems.

⼝口試委員會審定書........................................................................................................... #
誌謝.................................................................................................................................... i
中⽂文摘要........................................................................................................................... ii
ABSTRACT ..................................................................................................................... iii CONTENTS..................................................................................................................... iv
Chapter 1 Introduction................................................................................................ 1
Chapter 2 SU(2) Symmetry ......................................................................................... 3
2.1 Construct SU(2) Symmetry ........................................................................ 4
2.1.1 From SU(2) Higgs mechanism .............................................................. 4
2.1.2 Energy gap. .......................................................................................... 11
2.2 SU(2) in adjoint representation ...................................................................... 15
Chapter 3 SU(N) Symmetry ...................................................................................... 18
3.1SU(N) Mass Matrix ........................................................................................ 18
3.1.1 SU(N) Generators ................................................................................ 18
3.2Coupling to Fermion ...................................................................................... 20
3.2.1 Propogators .......................................................................................... 20
3.2.2 Feynman rules...................................................................................... 23
Chapter 4 Real system ............................................................................................... 25
4.1Iron pnictide ................................................................................................... 25
4.2Discussion ...................................................................................................... 26
Chapter 5 Conclusion ................................................................................................ 27
REFERENCE.................................................................................................................. 28
Appendix A ..................................................................................................................... 29
Appendix B ..................................................................................................................... 31
Appendix C ..................................................................................................................... 33

[1] Chyh-Hong Chern , Annals of Physics 350, 159 (2014)
[2] T. Shimojima , T. Sonobe, K. Ishizaka, Phys. Rev. B 89, 045101(2014)
[3] F. Buccella , H. Ruegg, Carlos A. Savoy, Nucl.Phys. B169 (1980) 68
[4] Ling Fong Li, Phys. Rev. D9 (1972) 1723
[5] Michael E. Peskin , Daniel V. Schroeder, “An introduction to Quantum field theory”(1995)
[6] Lewis H. Ryder, “Quantum field theory”(1996)
[7] Howard Goergi, “Lie Algebras in Particle Physics”(1999)
[8] https://en.wikipedia.org/wiki/Superconductivity
[9] https://en.wikipedia.org/wiki/BCS_theory
[10] https://en.wikipedia.org/wiki/High-temperature_superconductivity
[11] https://en.wikipedia.org/wiki/Quantum_spin_liquid

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