博碩士論文 972202006 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:25 、訪客IP:34.204.173.45
姓名 卓岱寧(Dai-Ning Cho)  查詢紙本館藏   畢業系所 物理學系
論文名稱
(Lie Algebra Contraction and Relativity Symmetries)
相關論文
★ 違反R-parity之超對稱標準模型下, 夸克-純量場一階費曼圖對中子電耦極矩之貢獻★ 無R超對稱標準模型中輕子的輻射衰變
★ 超對稱無R宇稱下的電子電偶極矩★ 龐加萊─史奈德相對論架構下的古典與量子力學
★ 伽利略座標下的電磁學與龐加萊-史奈德相對論下的電磁學★ Coherent state and co-adjoint orbits on irreducible representations of SU(4)
★ 無R宇稱超對稱裡的輕子味違反希格斯衰變★ 複數勞倫茲對稱
★ Wigner-Weyl′s transform and its contraction★ Effective Theories for Supersymmetric Nambu-Jona-Lasinio Models established through Functional Integration
★ Kähler Product and Symmetry Data in Quantum Mechanics
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 變形(deformation)作為李代數的數學工具,於近來被應用於推導量子相對論(Quantum Relativity)及其對應之架構;而壓縮(contraction)是做為另外一個李代數之下的數學工具,乃為變形的相反運算。在這篇論文中,我們著重於壓縮的基本概念以及數種主要運算過程,並加以適當的範例作為演示。我們首先將壓縮應用在目前科學界熟悉的五維時空,並得到許多作為可能容納動力學的時空。再來我們將壓縮應用於量子相對論的架構,並得到許多與前述時空相呼應的可能容納動力學的幾何結構。
摘要(英) Deformation as a mathematical tool is used in deducing the recently developed Quantum Relativity and its framework, whereas contraction is the operation opposite to against deformation. In this dissertation we focus on and illustrate the idea of contraction and discuss several general approaches to contraction in detail. We first use contraction as an illustration in deducing the algebras of the so-called possible kinematical groups under the framework of the SO(1,4) and SO(2,3) groups. Then we apply contraction under the framework of Quantum Relativity (SO(2,4)) and examine the algebras we obtained that may be of the kinematical groups in its framework.
關鍵字(中) ★ 李代數 關鍵字(英) ★ Cayley-Klein algebra
★ relativity symmetry
★ contraction
★ Lie algebra
論文目次 1 Introduction 1
2 Background 4
3 Contraction 11
3.1 General Formalism of Contraction 11
3.1.1 Wigner-Ino ̈nu ̈ Contraction 11
3.1.2 Generalized Wigner-Inonu Contraction 14
3.1.3 Graded Contraction 16
3.2 Bacry and Leblond’s Analysis of Possible Kinematics 20
3.2.1 The Method in the Paper 21
3.2.2 Description of SO(5) Contraction 26
3.3 Graded Contraction Focused on the Cayley-Klein Algebra 44
3.3.1 Grading Process of SO(N+1) Lie Algebra by Using Z_2^(⊗N) 44
3.3.2 Graded Contraction by Using the Cayley-Klein Lie Algebra 47
3.3.3 Description of the SO(5) Case 59
3.3.4 Connection of Graded and Generalized Contraction 64
4 Contraction in the Quantum Relativity Framework 70
4.1 Wigner-Inonu Contraction of SO(2,4) 70
4.2 One Step Further 80
4.3 Graded Contraction Focused on the Caley-Klein Algebra of SO(6) 85
5 Conclusion and Outlook 92
Bibliography 93
參考文獻 [1] H. S. Snyder, “Quantized Space-Time,” Phys. Rev. 71 38 (1947).
[2] G. Amelino-Camelia, “Testable scenario for relativity with minimum length,” phys. lett. B 510 255 (2001);  “Doubly-Special Relativity: First Results and Key Open Problems,” Int. J. Mod. Phys. D 11 35 (2002).
[3] J. Magueijo and L. Smolin, “Lorentz Invariance with an Invariant Energy Scale,” Phys. Rev. Lett. 88 190403 (2002); “Generalized Lorentz invariance with an invariant energy scale,” Phys. Rev. D 67 044017 (2003).
[4] J. Kowalski-Glikman and L. Smolin, “Triply special relativity,” Phys. Rev. D 70 065020 (2004); “Introduction to Doubly Special Relativity,” Lect. Notes Phys. 669 131 (2005).
[5] Y. Aharonov and T. Kaufherr, “Quantum Frames of References,” Phys. Rev. D 30 368 (1984).
[6] C. Rovelli, “Quantum reference systems,” Class. Quantum Grav. 8 317 (1991).
[7] Ashok Das and Otto C. W. Kong, “Physics of quantum relativity through a linear realization,” Phys. Rev. D 73, 124029 (2006).
[8] Otto C. W. Kong, “A deformed relativity with the quantum ħ,” Phys. Lett. B 665, 28 (2008).
[9] Otto C. W. Kong, “‘AdS5’ Geometry Beyond Space-time and 4D Noncommutative Space-time,” arXiv:0906.3581v1 [gr-qc] (2009).
[10] Otto C. W. Kong and Hung-Yi Lee, “‘Poincare-Snyder Relativity with Quantization,” arXiv:0909.4676v2 [gr-qc] (2010).
[11] E. Inonu and E. P. Wigner, “On the Contraction of Groups and Their Representations,” Proc. Nat. Acad. Sci. 39 510 (1953).
[12] E. Inonu, “A Historical Note on Group Contractions,” in http://www.physics.umd.edu/robot/wigner/inonu.pdf, Feza Gursey Institute, Istambul (1997).
[13] Henri Bacry and Jean-Marc Levy-Leblond, “Possible Kinematics,” J. Math. Phys. 9 1605 (1968).
[14] M. de Montigny and J. Patera, “Discrete and continuous graded contractions of Lie algebras and superalgebras,” J. Phys. A: Math. Gen. 24 525 (1991).
[15] M. de Montigny, J. Patera, and J. Tolar, “Graded contractions and kinematical groups of space-time,” J. Math. Phys. 35 405 (1994).
[16] Evelyn Weimar-Woods, “Contractions of Lie algebras: Generalized Inonu-Wigner contractions versus graded contractions,” J. Math. Phys. 36 4519 (1995).
[17] Francisco J. Herranz and Mariano Santander, “The general solution of the real  ℤ2⊗N graded contractions of SO(N+1),” J. Phys. A: Math. Gen. 29 6643 (1996).
[18] Angel Ballesteros, Francisco J. Herranz, Orlando Ragnisco and Mariano Santander, “Contractions, Deformations and Curvature,” Int. J. Theor. Phys. 47 649 (2008).
[19] Alice Fialowski and Marc de Montigny, “Deformations and contractions of Lie algebras,” J. Phys. A: Math. Gen. 38 6335 (2005).
[20] M. Planck, “Uber irreversible Strahlungsvorgange. Funfte Mitteilung,” Koniglich Preussiche Akademie der Wissenschaften (Berlin). Sitzungsberichte p. 440 (1899).
[21] J. Patera and H. Zassenhaus, “On Lie gradings.I,” Linear Algebra Appl. 112 87 (1989).
[22] Robert Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (John Wiley and Sons. Inc., 1941).
指導教授 江祖永(Otto C.W. Kong) 審核日期 2011-9-27
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明