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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃宇廷 | zh_TW |
| dc.contributor.advisor | Yu-tin Huang | en |
| dc.contributor.author | 劉友安 | zh_TW |
| dc.contributor.author | You-An Liu | en |
| dc.date.accessioned | 2023-08-15T17:10:37Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-15 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-02 | - |
| dc.identifier.citation | [1] K. S. Albayrak S. Towards the higher point holographic momentum space amplitudes. part ii. gravitons. Journal of High Energy Physics 2019.
[2] I. Antoniadis, A. Guillen, and F. Rondeau. Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms. JHEP, 01:043, 2023. [3] D. Baumann, W.-M. Chen, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel. Linking the singularities of cosmological correlators. JHEP, 09:010, 2022. [4] D. Baumann, C. D. Pueyo, A. Joyce, H. Lee, and G. L. Pimentel. The cosmological bootstrap: Spinning correlators from symmetries and factorization. 11(3), Sep 2021. [5] P. Benincasa and F. Cachazo. Consistency Conditions on the S-Matrix of Massless Particles. 5 2007. [6] N. E. J. Bjerrum-Bohr and O. T. Engelund. Gravitino interactions from yang-mills theory. 81(10), May 2010. [7] S. Choi, J. H. Shim, and H. Y. Song. Factorization of gravitational compton scattering amplitude in the linearized version of general relativity. 48(6):2953–2956, Sep 1993. [8] S. Corley. Massless gravitino and the ads-cft correspondence. 59(8), Mar 1999. [9] H. Elvang. Bootstrap and amplitudes: a hike in the landscape of quantum field theory. 84(7):074201–074201, Jul 2020. [10] D. Z. Freedman and A. Van Proeyen. Supergravity. Cambridge Univ. Press, Cam- bridge, UK, 5 2012. [11] G. W. Gibbons and S. W. Hawking. Action integrals and partition functions in quantum gravity. Phys. Rev. D, 15:2752–2756, May 1977. [12] H. Goodhew, S. Jazayeri, and E. Pajer. The cosmological optical theorem. 2021(04):021–021, Apr 2021. [13] H. S. Hartle JB. Wave function of the universe. Physical Review D [14] T. Hartman, D. Mazac, D. Simmons-Duffin, and A. Zhiboedov. Snowmass White Paper: The Analytic Conformal Bootstrap. In Snowmass 2021, 2 2022. [15] S. I. Heckelbacher T. Loops in ds/cft. Journal of High Energy Physics 2021. [16] M. Henneaux. Boundary terms in the AdS / CFT correspondence for spinor fields. In International Meeting on Mathematical Methods in Modern Theoretical Physics (ISPM 98), pages 161–170, 9 1998. [17] M. Kruczenski, J. Penedones, and B. C. van Rees. Snowmass White Paper: S-matrix Bootstrap. 3 2022. [18] J. Maldacena and G. L. Pimentel. On graviton non-gaussianities during inflation. 2011(9), Sep 2011. [19] D. A. McGady and L. Rodina. Higher-spin massless matrices in four dimensions. 90(8), Oct 2014. [20] D. O. Meltzer. The inflationary wavefunction from analyticity and factorization. 2021(12):018–018, Dec 2021. [21] R. V. Minces P. Energy and the ads/cft correspondence. Journal of High Energy Physics 2001. [22] W. Mück and K. S. Viswanathan. Conformal field theory correlators from classical field theory on anti–de sitter space: Vector and spinor fields. 58(10), Oct 1998. [23] NASA. Nasa’s webb takes star-filled portrait of pillars of creation. [24] T. Ortin. Gravity and Strings p. 865. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2nd ed. edition, 7 2015. [25] D. Poland and D. Simmons-Duffin. The conformal bootstrap. 12(6):535–539, Jun 2016. [26] S. Raju. New recursion relations and a flat space limit for ads/cft correlators. 85(12), Jun 2012. [27] M. D. Schwartz. Quantum Field Theory and the Standard Model. Cambridge University Press, 3 2014. [28] R. M. Wald. General Relativity, App. E.1,. Chicago Univ. Pr., Chicago, USA, 1984. [29] S. Weinberg. Quantum contributions to cosmological correlations. Phys. Rev. D, 72:043514, Aug 2005. [30] S. Weinberg. The Quantum theory of fields. Vol. 1: Foundations. Cambridge University Press, 6 2005. [31] J. W. York. Role of conformal three-geometry in the dynamics of gravitation. Phys.Rev. Lett., 28:1082–1085, Apr 1972. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88639 | - |
| dc.description.abstract | 在本論文中，我們考慮四維平坦空間等時關聯子的自舉。我們在平坦空間相關器中回顧了「宇宙光學定理」（COT），然後利用總能量為零和部分能量為零極限的約束、顯式局部性以及Ward-Takahashi恆等式對樹級關聯子進行約束。為了應用於費米子關聯子，我們推導出半整數算符的COT，並給出適用於Dirac和Majorana費米子的獨特規則，適用於宇宙的內部體積。 | zh_TW |
| dc.description.abstract | In this thesis, we consider the bootstrap of a four-dimensional flat space equal time correlator. we review the “Cosmological Optical Theorem” (COT) in the context of flat space correlators and proceed to constrain tree-level correlators using the constraints of total energy and partial energy poles, manifest locality, and Ward-Takahashi identities. To apply this to fermionic correlators, we derive the COT for half-integer operators and give distinctive rules suitable for Dirac and Majorana fermions in the bulk. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-15T17:10:37Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-15T17:10:37Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xv Chapter 1 Introduction 1 Chapter 2 Review of flat space correlators 3 2.1 Cosmological Correlation Function (in-in correlator) 4 2.2 Boundary Actions 6 2.3 Choice of Boundary conditions 9 2.4 Wave function coefficients (cosmological correlators) 13 Chapter 3 On-shell approach to correlators 19 3.1 Ward-Takahashi identities (WT identity) 19 3.2 Singularities and the cosmological optical theorem for flat space 21 3.2.1 Bosonic Field 24 3.2.2 Bosonic Partial Energy Pole 35 3.2.3 Dirac Fermion Field 36 3.2.4 Majorana Fermion Field 41 3.2.5 Fermionic Partial Energy pole 43 3.3 The bootstrap program 45 3.3.1 2pt correlators 45 3.3.2 3pt correlators 46 3.3.3 4pt correlators 47 Chapter 4 Bosonic correlators in Flat Spacetime 51 4.1 2pt correlators 51 4.2 3pt correlators 52 4.2.1 ⟨JO∗O⟩ 52 4.2.2 ⟨TOO⟩ 53 4.2.3 ⟨TTT⟩ 57 4.3 4pt correlators 58 4.3.1 ⟨OO∗OO∗⟩ exchanging photon 60 4.3.2 ⟨JOJO∗⟩ 62 4.3.3 ⟨OOOO⟩ exchanging graviton 65 4.3.4 ⟨TOTO⟩ 71 Chapter 5 Fermionic correlators in Flat Spacetime 81 5.1 2pt correlators 81 5.1.1 Massless Spin Half Fermion 81 5.1.2 Gravitino 82 5.2 3pt correlators 83 5.2.1 ⟨Jχ¯−χ+⟩ 83 x doi:10.6342/NTU202302262 5.2.2 ⟨T χ¯−χ+⟩ 85 5.2.3 ⟨T ψ¯−ψ+⟩ 85 5.3 4pt correlators 88 5.3.1 ⟨Jχ¯−Jχ+⟩ . 88 5.3.2 ⟨T χ¯−Tχ+⟩ 92 5.3.3 ⟨T ψ¯−T ψ+⟩ 107 5.4 SUSY Ward Identity Bootstrap 125 5.4.1 ⟨T ψ¯ψ⟩ 125 5.4.2 ⟨T ψ¯T ψ⟩ 127 5.5 ⟨ψ¯ψψ¯ψ⟩ and Majorana condition 129 Chapter 6 Conclusion 131 References 133 Appendix A — Notation 137 A.1 Commutation 137 A.2 Vector Indices 138 A.2.1 4D metric 138 A.2.2 4D vector 138 A.2.3 3D vector 138 A.3 Spin 1/2 polarization and classical field 139 A.3.1 Gamma Matrices 139 A.3.2 4D spin 1/2 representation 139 A.3.3 Momentum notation 140 A.3.4 Dirac Equation 142 A.3.5 Dirac Equation Solution (4D fermionic polarization) 142 A.3.6 3D Boundary Field (3D asymptotic state for correlator, 3D polariza- tion) and Related 4D Classical Solution 143 A.3.7 Majorana fermions and its images in 3D boundary 145 A.4 Amplitude notation 146 A.5 (Uncontracted) Cosmological Correlator, Contracted Cosmological Correlator and in-in correlator 148 Appendix B — Cosmological Background and Wave Function 151 Appendix C — Feynman rules from eiScl 155 C.1 Feynman Rule from Bulk Action 155 C.2 Bounary Action 158 C.3 Fermionic Feynman Rule from Boundary Action 170 Appendix D — Correlator Calculation by the Lagrangian Approach 179 D.1 scalar QED : ⟨JO∗O⟩ and ⟨JO∗JO⟩ 179 D.1.1 ⟨JO∗O⟩ 180 D.1.2 ⟨JO∗JO⟩ 181 D.2 TOO 184 D.3 QED : ⟨Jχ¯χ⟩ and ⟨Jχ¯Jχ⟩ 186 D.4 T χ¯χ 194 Appendix E — Ward Identity of the Amplitude 199 E.1 Spin 1 field 199 E.2 Spin 2 field 200 Appendix F — Ward Takahashi Identities of the Correlator 201 F.1 2pt WT identity 201 F.2 3pt WT identity 202 F.3 4pt WT identity 206 Appendix G — Total Energy Pole 213 | - |
| dc.language.iso | en | - |
| dc.subject | 半自旋 | zh_TW |
| dc.subject | 宇宙學關聯子 | zh_TW |
| dc.subject | 自舉 | zh_TW |
| dc.subject | 邊界項 | zh_TW |
| dc.subject | 伴重力子 | zh_TW |
| dc.subject | 平直時空 | zh_TW |
| dc.subject | Gravitino | en |
| dc.subject | Spin Half | en |
| dc.subject | Cosmological Correlator | en |
| dc.subject | Boundary term | en |
| dc.subject | Flat Space | en |
| dc.subject | Bootstrap | en |
| dc.title | 平直時空的宇宙關聯子 | zh_TW |
| dc.title | Flat Space Cosmological Correlator | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳恒榆;賀培銘;Daniel Baumann | zh_TW |
| dc.contributor.oralexamcommittee | Heng-Yu Chen;Pei-Ming Ho;Daniel Baumann | en |
| dc.subject.keyword | 宇宙學關聯子,半自旋,伴重力子,平直時空,邊界項,自舉, | zh_TW |
| dc.subject.keyword | Cosmological Correlator,Spin Half,Gravitino,Flat Space,Boundary term,Bootstrap, | en |
| dc.relation.page | 214 | - |
| dc.identifier.doi | 10.6342/NTU202302262 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-08-04 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| 顯示於系所單位： | 物理學系 | |
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