Position Spacetime Description of Scalar Kirchhoff Diffraction

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题名:	Position Spacetime Description of Scalar Kirchhoff Diffraction
作者:	陳佳恩;Chen, Jia-En
贡献者:	物理學系
关键词:	克希荷夫繞射;Kirchhoff Diffraction
日期:	2025-06-26
上传时间:	2025-10-17 11:53:30 (UTC+8)
出版者:	國立中央大學
摘要:	本篇論文中，我們將在(3+1)維閔可夫斯基時空與微彎曲時空下用克希荷夫積分探討純量場繞射的時空描述。在無重力的閔可夫斯基時空中，繞射理論在頻率空間下已經發展得相當完備。然而，從基礎理論的觀點來看，繞射是波傳播產生的現象，也就是說時間是不可或缺的因素。繞射中的因果關係可以從此時空描述中展現。在閔可夫斯基時空下，我們提供完備且精確的克希荷夫繞射公式與兩個明確例子:無限半平面和單位圓盤問題。閔可夫斯基時空的分析實際上是由微彎曲時空中的重力透鏡啟發。克希荷夫繞射也適用於描述重力透鏡現象，其中因果關係會因為重力而被修正。儘管我們還未完成微彎曲時空的一般分析，我們將提供一個簡化的例子說明過一質點的軸上類光繞射。;In this thesis, we formulate the position spacetime description of the scalar diffraction theory using the Kirchhoff integral in (3+1)D Minkowski and weakly curved spacetime. For the Minkowski case, without gravity, the diffraction theory has been developed concretely in frequency space. However, from fundamental physics point-of-view, diffraction is a phenomenon caused by wave propagation, which means that time is a significant ingredient as well. The causality encoded in diffraction processes can thus be presented in this spacetime description. In Minkowski spacetime, we provide a complete and exact formulation of Kirchhoff diffraction with two explicit examples – infinite half-plane and unit circular disk problems. The Minkowski analysis is in fact motivated by gravitational lensing in weakly curved spacetime, which can also be formulated in terms of Kirchhoff diffraction. The causality is corrected by the existence of gravity. Although we have not completed the general analysis in weakly curved spacetime, a simplified example of on-axis null diffraction through a point mass will be provided.
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