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研究生： 張晉嘉
Chang, Chin-Chia
論文名稱： 實三維空間中的變形量子化
On the Deformation Quantization on R^3
指導教授： 吳思曄
Wu, Siye
口試委員: 何南國
Ho, Nan-Kuo
鄭日新
Cheng, Jih-Hsin
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 27
中文關鍵詞： 變形量子化 、Gutt 乘積 、＊乘積
外文關鍵詞： deformation quantization, Gutt product, star product
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    • 在這篇論文我們會透過實四維空間中的 Moyal 乘積經由 U(1)作用下來定義 一個實三維空間中的 ∗ 乘積。這個我們定的 ∗ 乘積與既有在 su(2)的對偶李代數 上的 Gutt 乘積同為實三維空間中的 ∗ 乘積在算數上有不同結果。我們將證明他 們是等價的並且構造出等價算子。

    In this thesis, we define a star product on R^3 which is associated to the Moyal product on R^4. We also recall the Gutt product defined on the dual of a Lie algebra. Under the isomorphism between the dual of su(2) and R^3, we construct an equivalence operator between these two star products.

    1 Introduction . . . . . . . . . . . .1 2 Star product on R^3 . . . . . . . . . . . .3 3 Gutt prodcut. . . . . . . . . . . . 7 4 Equivalence . . . . . . . . . . . .10 4.1 Equivalence in the homological language . . . . . . . . . . . . 10 4.2 Weyl product ........................... 12 4.3 Construction of the equivalence operator . . . . . . . . . . . . 17 A Smoothness of the star product . . . . . . . . . . . .25

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