(54.236.58.220) 您好!臺灣時間:2021/02/27 11:28
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:周士凱
研究生(外文):Shih-Kai Chou
論文名稱:量子色動力學手則相變之重整化群研究
論文名稱(外文):A Study of QCD Chiral Phase Transition with the Renormalization Group
指導教授:趙挺偉趙挺偉引用關係
指導教授(外文):Ting-Wai Chiu
口試委員:高涌泉賀培銘
口試委員(外文):Yeong-Chuan KaoPei-Ming Ho
口試日期:2014-07-17
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:2014
畢業學年度:102
語文別:中文
論文頁數:59
中文關鍵詞:手則對稱量子色動力學手則相變重整化群
外文關鍵詞:chiral symmetryQCD chiral phase transitionrenormalization group
相關次數:
  • 被引用被引用:0
  • 點閱點閱:75
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
量子色動力學 (quantum chromodynamics, QCD) 是一描述夸克和膠子交互作用的基本理論。在零溫度下,N_f 個無質量夸克的手則對稱因 QCD 真空而破缺,且軸 U(1) 對稱因軸畸異 (axial anomaly) 而破缺。手則對稱與軸 U(1) 對稱兩者在高溫時均期望會被還原。在此論文中,我們以 QCD 的等效場論,也就是 N_f = 2 之 SU(N_f) × SU(N_f) 線性 σ 模型,計算其包含所有耦合項的 β 函數至一階迴圈來研究手則對稱與軸 U(1) 對稱的還原。

Quantum chromodynamics (QCD) is the fundamental theory for the interaction between quarks and gluons. At zero temperature, the chiral symmetry of N_f massless quarks is broken by the vacuum of QCD, and the axial U(1) symmetry is broken by the axial anomaly. It is expected that the chiral symmetry and the axial U(1) symmetry both are restored at high temperature. In this thesis, we study the restorations of the chiral symmetry and the axial U(1) symmetry in the effective field theory of QCD, namely, the SU(N_f)_L x SU(N_f)_R linear σ model for N_f = 2, by computing the β functions of all couplings to the one-loop order.

口試委員審定書 i
誌謝 ii
摘要 iii
Abstract iv
Introduction 1
Chiral Symmetry in QCD 4
Spontaneous Breaking of Chiral Symmetry 7
The U(1)_A Problem 8
The σ Model 9
The U(N_f)_L x U(N_f)_R Linear σ Model 13
The SU(N_f)_L x SU(N_f)_R Linear σ Model 16
Order of The Chiral Phase Transition 19
The β Function of the SU(2)_L x SU(2)_R Linear σ Model 23
Effects of Approximate U(1)_A Restoration 36
Conclusions 40
Bibliography 41
Appendix 44
The Structure of the β Function 44
The One-Loop Structure of φ4 Theory 46
Dimensional Regularization: The Form of Renormalization Constants 51
Minimal Subtraction Scheme 51
The β Functions with Several Couplings 53
Renormalization Group Analysis 54
The Fixed Point 55
The Stability Matrix 57


[1] Kohsuke Yagi,Tetsuo Hatsuda, and Yasuo Miake, Quark-Gluon Plasma, Cambridge University Press, 2005.
[2] Robert D. Pisarski and Frank Wilczek, “Remarks on the Chiral Phase Transition in Chromodynamics”, Phys. Rev. D 29, 338 (1984).
[3] Sinya Aoki, Hidenori Fukaya, Yusuke Taniguchi, “1st or 2nd; the Order of Finite Temperature Phase Transition of N_f = 2 QCD from Effective Theory Analysis”, arXiv/1312.1417 [hep-lat] (2013).
[4] C. Gattringer and C.B. Lang, Quantum Chromodynamics on the Lattice: An Introductory Presentation, Springer, 2010.
[5] A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, “Pseudoparticle Solutions of the Yang-Mills Euations”, Phys. Lett. B 59, 85 (1975).
[6] G. ’t Hooft, “Symmetry Breaking through Bell-Jackiw Anomalies”, Phys. Rev. Lett. 37, 8 (1976); G. ’t Hooft, “Computation of the Quantum Effects due to a Four- Dimensional Pseudoparticle”, Phys. Rev. D 14 3432 (1976); G. ’t Hooft, “Erratum/ Computation of the Quantum Effects due to a Four-Dimensional Pseudoparticle”, Phys. Rev. D 18 2199 (1978).
[7] Khalil M. Bitar and Shau-Jin Chang, “Vacuum Tunneling of Gauge Theory in Minkowski Space”, Phys. Rev. D 17, 486 (1978).
[8] M. Gell-Mann and M. Levy, “The Axial Vector Current in Bety Decay”, Nuovo Cimento 16, 705 (1960).
[9] Jean Zinn-Justin, Quantum Field Theory and Critical Phenomena (Fourth Edition), Oxford University Press, 2002.
[10] Frank Wilczek, “Application of the Renormalization Group to a Second-Order QCD Phase Transition”, Int. J. Mod. Phys. A, 07, 3911 (1992)
[11] A. Butti, A. Pelissetto, and E. Vicari, “On the Nature of the Finite-Temperature Transition in QCD”, J. High Energy Phys. 08, 029 (2003).
[12] Sinya Aoki, Hidenori Fukaya, and Yusuke Taniguch, “Chiral Symmetry Restoration, the Eigenvalue Density of the Dirac Operator, and the Axial U(1) Anomaly at Finite Temperature”, Phys. Rev. D 86, 114512 (2012).
[13] A. J. Paterson, “Coleman-Weinberg Symmetry Breaking in the Chiral SU(n) × SU(n) Linear σ Model”, Nucl. Phys. B 190 [FS3], 188 (1981).
[14] P. Bak, S. Krinsky, and D. Mukamel, “First-Order Transitions, Symmetry, and the ε Expansion”, Phys. Rev. Lett. 36, 52 (1976).
[15] Kleinert Hagen, Verena Schulte-Frohlinde, Critical Properties of φ^4 Theories, World Scientific, 2001.
[16] Michael E. Peskin, Dan V. Schroeder, An Introduction To Quantum Field Theory, Westview Press, 1995.
[17] Kenneth G. Wilson, “The Renormalization Group and Critical Phenomena”, Rev. Mod. Phys. 55, 583 (1983).
[18] N. Goldenfeld, Lectures on Phase Transitions and Critical Phenomena, Westview Press, 1992.
[19] Daniel J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena, World Scientific, 1984.
[20] Michael Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction, Wiley Interscience, 1989.

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔