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標題: | 從古典散射衝量去得出電磁任意子以及三維重力的散射振幅 Use classical scattering impulse to find quantum scattering amplitude of electromagnetic anyon and scattering amplitude of gravity in the (2+1) dimension |
作者: | 莊文瑜 Wen-Yu Chuang |
指導教授: | 黃宇廷 Yu-Ting Huang |
關鍵字: | 散射振幅,散射衝量,任意子, scattering amplitude,scattering impulse,anyon, |
出版年 : | 2024 |
學位: | 碩士 |
摘要: | 在量子場論中,我們曾經學過如何計算不同物理場下的散射振幅,同時我們也知道如何從散射振幅去推導出不同物理場下的散射截面。在此篇文章中會介紹如何用散射振幅去推導出古典的散射衝量,並且使用這個方式從古典散射衝量去回推出散射振幅。在 (2+1) 維的時空中,有一些情況我們無法使用費曼規則去得出他們的散射振幅。第一個例子就是重力在 (2+1) 維的情況,由於重力在 (2+1) 維的時候沒有任何動態自由度,所以我們無法畫出費曼圖。但是,重力在 (2+1) 維的散射衝量並不為零,因此我們可以使用上面提到的方法從散射衝量去回推散射振幅。另一個例子是任意子–一種只會出現在 (2+1) 維時空且自旋並非整數或半整數的粒子。由於任意子並非基本粒子,所以我們無法使用費曼圖來算出散射振幅。但是同樣的,由於任意子的散射衝量並不為零,所以我們可以用上述方法得出散射振幅。 In quantum field theory, we have learned how to calculate the scattering amplitude by drawing Feynman diagrams and then using Feynman rules to calculate the contribution of each diagram to the scattering amplitude. Besides, we have also learned how to use the scattering amplitude to derive the cross section which is a classical observable. However, in the (2+1) dimension, there are some special cases in which we can’t define Feynman rules. For example, gravity in the (2+1) dimension has no dynamic degree of freedom. However, we can see there are non-trivial physical observables that reflect the effect of gravity such as the impulse of a particle going through a gravitational source. Another example is the scattering amplitude of anyon which is a special kind of particle in (2+1) dimension. Since the spin of anyon can be an arbitrary number, it is not an elementary particle and we can’t define its Feynman rules either. As gravity in (2+1) dimension, the impulse of particles going through a source composed of anyon is also non-trivial. Therefore, we can calculate the scattering impulse of the above two cases and try to use the scattering impulse to derive the scattering amplitude of them. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92536 |
DOI: | 10.6342/NTU202400820 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 物理學系 |
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