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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 細道和夫(Kazuo Hosomichi) | |
| dc.contributor.author | Tsung-Yen Chen | en |
| dc.contributor.author | 陳宗彥 | zh_TW |
| dc.date.accessioned | 2021-05-13T06:41:54Z | - |
| dc.date.available | 2017-07-20 | |
| dc.date.available | 2021-05-13T06:41:54Z | - |
| dc.date.copyright | 2017-07-20 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-05-24 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2551 | - |
| dc.description.abstract | 本論文總結了關於應用resurgence trans-series 在量子力學和量子場論的知識。我們重現了在微擾級數中的虛數項和瞬子-反瞬子對中的虛數項的相消。結合所有來自非微擾半古典組態的貢獻之後，就可以構築出所謂的trans-series。因為紅外重整子的存在，在量子場論中構建trans-series被認為是無法實現的。近年來，因為在某些被緊湊化後的量子場論中發現了新的半古典組態，這些半古典組態被認為可能對應到紅外重整子。利用trans-series來給部分量子場論在弱藕荷常數極限下一個非微擾的定義可能是可以實現的。 | zh_TW |
| dc.description.abstract | This thesis reviews the idea of resurgence trans-series and its application on Quantum mechanics and Quantum field theory. The cancellation between the imaginary part of the perturbative series and the imaginary part of the instanton-anti-instanton configuration in quantum mechanics is shown. Combining all the contribution from the non-perturbative semiclassical configuration, the so-called trans-series can be constructed. Because of the existence of IR renormalon, the construction of trans-series in QFT was not thought to be valid. In recent years, new semiclassical configurations have been found in some compactified theories. Those configurations are thought to be corresponded to the elusive IR renormalons. A non-perturbative definition of a class of field theories by the trans-series in the weak coupled limit may be possible. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T06:41:54Z (GMT). No. of bitstreams: 1 ntu-106-R04222038-1.pdf: 1234877 bytes, checksum: 044d796b53413fbb920a60e670279d63 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 1 Introduction 1
2 Perturbation series 3 2.1 Borel resummation 5 2.2 Source of divergence 7 2.2.1 Renormalon divergence 9 2.3 Trans-series approach 13 3 Resurgence in QM 16 3.1 Quantum mechanics in the anharmonic oscillator 17 3.2 Quantum mechanics in the double well potential 19 3.2.1 One instanton contribution 21 3.2.2 Multi instanton contribution 25 4 Resurgence in QFT 31 4.1 QCD(adj) on R3 S1 32 4.1.1 4-d theory 33 4.1.2 3-d eective theory 34 4.1.3 Topological congurations on R3 S1 39 4.1.4 Topological molecules and IR renormalons in QCD(adj) on R3 S1 42 4.2 CPN-1 model on R1 S1 44 4.2.1 CPN-1 model 45 4.2.2 Gauge holonomy 46 4.2.3 Free energy 48 4.2.4 Topological congurations on R1 S1 48 4.2.5 IR renormalons and bions 56 5 Conclusion and Future directions 61 Appendices 62 A Ambiguity of Borel resummation 62 B Computation of the functional determinant in Quantum Mechanics 64 Appendix B.A Gelfand-Yaglom method 66 Bibliography 70 | |
| dc.language.iso | en | |
| dc.subject | 瞬子 | zh_TW |
| dc.subject | trans-series | zh_TW |
| dc.subject | 微擾展開 | zh_TW |
| dc.subject | 重整子 | zh_TW |
| dc.subject | Resurgence | zh_TW |
| dc.subject | Borel resummation | zh_TW |
| dc.subject | Resurgence | en |
| dc.subject | perturbative expansion | en |
| dc.subject | trans-series | en |
| dc.subject | renormalon | en |
| dc.subject | instanton | en |
| dc.subject | Borel resummation | en |
| dc.title | 在量子力學和量子場論中的Resurgence | zh_TW |
| dc.title | Resurgence in Quantum Mechanics and Quantum Field Theory | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳恒榆(Heng-Yu Chen),賀培銘(Pei-Ming Ho) | |
| dc.subject.keyword | Resurgence,Borel resummation,瞬子,重整子,微擾展開,trans-series, | zh_TW |
| dc.subject.keyword | Resurgence,Borel resummation,instanton,renormalon,perturbative expansion,trans-series, | en |
| dc.relation.page | 73 | |
| dc.identifier.doi | 10.6342/NTU201700825 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2017-05-24 | |
| 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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