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研究生： 陳建羽
Chien-Yu Chen
論文名稱： e+e- → γγ in noncommutative electroweak model
非線性交換幾何電弱模型下正負電子對撞
指導教授： 耿朝強
Chao-Qiang Geng
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2006
畢業學年度： 94
語文別： 英文
論文頁數： 49
中文關鍵詞： 弦論 、時空不對易 、非線性交換幾何 、非線性交換幾何場論
外文關鍵詞： string theory, noncommutative spacetime, noncommutative geometry, noncommutative field theory
相關次數： 點閱：58  下載：0 
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    • 我們簡介一些在非線性交換電弱模型下 e+e- --> e+e-, e+e- --> e-e- 和 e+e- --> γγ 線性碰撞的過程. 我們發現Ward identity在 e+e- --> γγ 過程中不會自動被滿足. 雖然這個理論沒有UV的問題,但還是仍然會破壞么正對稱性,而為了要解決這類的問題必須限制背景電場為零,背景張量場內積大於等於零和第一階 θ 必須不存在,使得因果關係, 么正性和規範對稱被滿足.

    We study some tree level processes, such as e+e− → e+e−, e−e− → e−e− and e+e− → γγ in the noncommutative electroweak model. We find that the process of e+e− → γγ does not automatically satisfy the Ward identity. To solve this problem, we assume θ0i = ~E 2 NC = 0, θµνθµν > 0 and the vanishing first order θ terms. The constrains of θ0i= ~E 2 NC = 0 and θµνθµν > 0 are used to solve the causality and unitary problems, although such theories are free of ultraviolet divergence but they still violate unitarity.

    1 Introduction . . . . . . . . . . . . . . . . . . . . . .4 2 Brief Introduction to Noncommutative String . . . . . . 7 3 Gauge theory in noncommutative spacetime . . . . . . . 10 4 U(1) Noncommutative QED Model . . . . . . . . . . . . .17 5 Noncommutative electroweak model . . . . . . . . . . . 19 5.1 U(3)⋆⊗U(2)⋆⊗U(1)⋆. . . . . . . . . . . . . . . . .21 5.2 SU(3)⊗SU(2)⊗U(1) . . . . . . . . . . . . . . . . 23 6 The symmetry on noncommutative space time . . . . . . 26 7 e+ e− collisions in NCQED model . . . . . . . . . . . 28 7.1 The Feymann rules of U(1) NCQED . . . . . . . . . .28 7.2 The Bhabha scattering process in NCQED . . . . . . 29 7.3 The M ぴoller scattering process in NCQED . . . . .30 7.4 The pair annihilation process in NCQED . . . . . . 31 7.5 The Compton scattering process in NCQED . . . . . .33 8 e+ e− collisions in NCEW model . . . . . . . . . . . .34 8.1 The feynman rules of the θ deformed NCEW . . . . .34 8.1.1 The minimal NCEW . . . . . . . . . . . . . . . . 34 8.1.2 The non-minial NCEW . . . . . . . . . . . . . . .35 8.2 The Bhabha scattering process in NCEW . . . . . . .36 8.3 The M ぴoller scattering process in NCEW . . . . . 38 8.4 The pair annihilation process in NCEW . . . . . . .40 8.5 The Compton scattering process in NCEW . . . . . . 45 9 Conclusion . . . . . . . . . . . . . . . . . . . . . . 47

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