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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳恒榆(Heng-Yu Chen) | |
| dc.contributor.author | Lung-Chuan Chen | en |
| dc.contributor.author | 陳隆全 | zh_TW |
| dc.date.accessioned | 2021-06-17T08:10:57Z | - |
| dc.date.available | 2021-02-20 | |
| dc.date.copyright | 2021-02-20 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-02-17 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73816 | - |
| dc.description.abstract | 在本論文中，我們將歐幾里得情景下的鑲嵌形式(embedding formalism)拓展至勞倫茲情景以描述勞倫茲反德西特空間下的對稱無跡張量。利用此形式，我們藉由兩由塊到邊界傳播子來建立諧和函數。經由此方式所建構的諧和函數可被表示成能被陰影轉換(shadow transform)與自旋陰影轉換(spin-shadow transform)所聯繫的由塊至塊傳播子的線性組合。此外，我們也建構了在勞倫茲情景下傳遞帶質量自旋場的由塊至塊傳播子的分裂表示(split representation)。在這表示中，該傳播子被表示成諧和函數的線性組合。作為初步應用，我們運用該傳播子計算描述任意純量一次運算子(primary operator)間的四點樹狀維騰圖(Witten diagram)。該計算結果可表示成共形部分波的形式，意指其可表示成兩個三點相關函數的內積積分。 | zh_TW |
| dc.description.abstract | In this work, we extend the embedding formalism developed in Euclidean signature to Lorentzian case to describe the symmetric traceless tensors in Lorentzian Anti-de sitter space. Using this formalism, we construct the harmonic function by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. The harmonic functions constructed in this way are shown to be the linear combination of bulk-to-bulk propagators which are related to each other by the so-called shadow transform and spin-shadow transform. Furthermore, We developed the split representation of the bulk-to-bulk propagators of massive spinning fields in Lorentzian signature, the propagators are expressed as a linear combination of harmonic functions. As a application, we computed the tree-level four-point Witten diagram describing spin J exchange between scalar primaries of arbitrary dimension. The Witten diagrams eventually could be related to the conformal partial wave, which is defined as the integral of the product of two three-point functions. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T08:10:57Z (GMT). No. of bitstreams: 1 U0001-2801202122393200.pdf: 28351952 bytes, checksum: c2147817986d08ae3878ee4cc22ff4d9 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i Acknowledgements iii 摘要v Abstract vii Contents ix List of Figures xi List of Tables xiii Chapter 1 Introduction 1 Chapter 2 Euclidean AdS propagators and split representation 5 2.1 Embedding formalism . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Euclidean AdS propagators . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Euclidean AdS Split Representation . . . . . . . . . . . . . . . . . . 11 Chapter 3 Representation theory of conformal group 15 3.1 Representation theory of conformal group in Euclidean signature . . 15 3.2 Representation theory of conformal group in Lorentzian signature and Weyl reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 4 Lorentzian AdS harmonic function 21 4.1 Construction of Lorentzian AdS harmonic function . . . . . . . . . . 23 4.2 Orthogonality of Lorentzian harmonic function . . . . . . . . . . . . 36 4.3 Completeness relation and split representation . . . . . . . . . . . . . 46 Chapter 5 The computation of Witten diagrams 49 5.1 Threepoint Witten diagrams . . . . . . . . . . . . . . . . . . . . . . 49 5.2 Fourpoint Witten diagrams . . . . . . . . . . . . . . . . . . . . . . 55 Chapter 6 Conclusion 63 References 65 Appendix A — Conformal P integral in Lorentzian space 71 Appendix B — Conformal Z integral in Lorentzian space 75 Appendix C — The Derivation of multinomial theorem for noninteger power 79 | |
| dc.language.iso | en | |
| dc.subject | 分裂表示 | zh_TW |
| dc.subject | 反德西特/共形場論對偶 | zh_TW |
| dc.subject | 鑲嵌形式 | zh_TW |
| dc.subject | 自旋傳播子 | zh_TW |
| dc.subject | 維騰圖 | zh_TW |
| dc.subject | Split Representation | en |
| dc.subject | embedding formalism | en |
| dc.subject | AdS/CFT | en |
| dc.subject | Spinning AdS propagator | en |
| dc.subject | Witten diagram | en |
| dc.title | 勞侖茲反德西特空間中之自旋傳播子 | zh_TW |
| dc.title | Spinng AdS propagators in Lorentzian Anti-de Sitter space | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 109-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 賀培銘(Pei-Ming Ho),黃宇廷(Yu-tin Huang) | |
| dc.subject.keyword | 反德西特/共形場論對偶,分裂表示,維騰圖,自旋傳播子,鑲嵌形式, | zh_TW |
| dc.subject.keyword | AdS/CFT,Split Representation,Witten diagram,Spinning AdS propagator,embedding formalism, | en |
| dc.relation.page | 81 | |
| dc.identifier.doi | 10.6342/NTU202100241 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2021-02-17 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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