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  • 學位論文

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

摘要


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。

並列摘要


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.

參考文獻


[1] D. Arnal, Le produit star de Kontsevich sur le dual d’une alg`ebra de Lie nilpotente, C. R. Acad. Sci. Paris, S ́er. I, Math. 327, 823–826 (1998).
[2] D. Arnal, N. Ben Amar and M. Masmoudi, Cohomology of good graphs and Kontsevich linear star products, Lett. Math. Phys. 48, 291–306 (1999).
[3] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer,
Deformation theory and quantization, I, Deformations of symplectic structures, Ann. Phys. (N.Y.) 111, 61–110 (1978).
[4] A. Connes, M. Flato and D. Sternheimer, Closed star products and cyclic cohomology, Lett. Math. Phys. 24, 1–12 (1992).

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