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研究生:王浚帆
研究生(外文):Juven Wang
論文名稱:量子色動力學有效場論之Π介子的體積黏滯係數
論文名稱(外文):Bulk Viscosity of Pion Gas by Chiral Perturbation Theory and Boltzmann Equation
指導教授:陳俊瑋陳俊瑋引用關係
指導教授(外文):Jiunn-Wei Chen
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:2008
畢業學年度:96
語文別:英文
論文頁數:87
中文關鍵詞:量子色動力學相圖有效場論Π介子氣體黏滯係數流體力學熱力學量子場論量子力學物理
外文關鍵詞:Quantum Chromodynamics(QCD) phase diagramChiral Perturbation Theory(ChPT)Pion gasViscosityHydrodynamicsThermodynamicsQuantum Field TheoryQuantum Mechanics
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  • 收藏至我的研究室書目清單書目收藏:0
量子色動力學下的多體問題與凝態物理是目前量子色動力學的前瞻研究領域。量子色動力學的相圖即是上述領域中現正熱絡發展的例子[可參考Rajagopal和Wilczek(Wilczek 是2004 Nobel Prize Winner in Physics)的論文]。其中熱力學性質與流體力學性質有可能是量子色動力學相圖的良好指標。
在此篇碩士論文裡面,我們從量子力學相圖中鎖定無化學位能的強子相態的區域,研究了Π介子氣體的體積黏滯係數(流體力學參數)與亂度(熱力學參數)。而Π介子氣體本身是在低能量狀態量子色動力學相中的最主要的物質。我們也會討論切黏滯係數(或剪應力黏滯係數,為流體力學參數)來與體積黏滯係數做比較。藉由一套量子色動力學的有效量子場論方法(手徵微擾場論或對掌性微擾場論),以及運用玻茲曼方程式,我們進一步地研究了無質量Π介子氣體(即在手徵極限或對掌性極限下的情況;arXiv: 0711.4842)與一般質量Π介子氣體的體積黏滯係數。
Many body Quantum Chromodynamics(QCD) and condensed matter physics of QCD are frontiers of advance research of QCD. Research on QCD Phase Diagram is an example for these thriving fields [see Rajagopal and Wilczek]. Particularly thermodynamic properties and hydrodynamic properties might be good indices for QCD phase diagram. We have studied the bulk viscosity(hydrodynamic quantity) and entropy(thermodynamic quantity) of pion gas(the dominant configuration of QCD at low temperature) in the hadronic phase with zero chemical potential. We will also mention shear viscosity(hydrodynamic quantity) for comparison with bulk viscosity. By using Chiral Perturbation Theory of QCD, and applying relativistic Boltzmann equation, we examine the bulk viscosity of massless pion case (in the chiral limit; arXiv: 0711.4842) and massive pion case.
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 QCD Phase Diagram . . . . . . . . . . . . . . . . . . 4
1.3 Thermodynamics . . . . . . . . . . . . . . . . . . . . 5
1.4 Hydrodynamics . . . . . . .. . . . . . . . . . . . . . 5
1.5 Boltzmann Equation . . . . . . . . . . . . . . . . . . 7
1.6 Formulations of Viscosities from Hydrodynamics and Boltzmann Equation . . . . 9
1.6.1 Viscosities in the forms of distribution function . . . . . . . . . . . . . . . 9
1.6.2 Distribution function solved from Boltzmann Equation . . . . . . . . . . . 10
1.7 Chiral Perturbation Theory of QCD and its Lagrangian. 11
1.7.1 Chiral Perturbation Theory Lagrangian . . . . . . 12
1.7.2 Scattering Amplitude. . . . . . . . . . . . . . . . 14
2 Pion Bulk Viscosity of 2 Pions-2 Pions Scattering Process 16
2.1 Massless Pions Case (the Chiral Limit) . . . . . . . 16
2.1.1 Thermodynamics of Massless Pion Gas . . . . . . . . 16
2.1.2 Massless Pion Bulk Viscosity . . . . . . . . . . . 16
2.2 Massive Pions Case. . . . . . . . . . . . . . . . . . 21
2.2.1 Highly Non-Relativistic Limit (T << m or T!=0). . . 22
2.2.2 Low Temperature Behavior (T < m). . . . . . . . . . 23
2.2.3 High Temperature Behavior (T > m) . . . . . . . . . 24
3 Conclusion 27
4 Appendix: Pion Bulk Viscosity including 2 Pions-4 Pions Scattering Process
4.1 Chiral Perturbation Theory Lagrangians of 2 pions, 4 pions and 6 pions terms . . . . . . . . . 30
4.1.1 Scattering Amplitude Including 2 Pions-4 Pions Scattering Process . . . . 30
4.2 Isovectors and Isoscalars . . . . . . . . . . . . . . 42
4.2.1 Isovectors and Isoscalars Two Pions State . . . . . 42
4.2.2 Isovectors of Four Pions State. . . . . . . . . . . 44
Bibliography 87
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[2] M. A. Stephanov, arXiv:hep-lat/0701002 (2007).
[3] J.W. Chen and J. Wang, arXiv:0711.4842 (2007)
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Mechanics (John Wiley&Sons, 1987)
[6] J. D. Bjorken, Phys. Rev. D 27, 140 (1983)
[7] E. Nakano, hep-ph/0612255 (2006)
[8] S. Scherer, hep-ph/0210398 (2002)
[9] P. Gerber and H. Leutwyler, Nucl. Phys. B 321, 387 (1989).
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[12] D. Kharzeev and K. Tuchin, arXiv:0705.4280 [hep-ph] (2007).
[13] H. B. Meyer, arXiv:0710.3717 [hep-lat] (2007).
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