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古典及び量子(2+1)次元重力の位相的側面
https://doi.org/10.11501/2964193
https://doi.org/10.11501/29641935c05a50e-397a-496f-94dc-0478f284cd23
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
diss_ko831.pdf (23.9 MB)
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| Item type | デフォルトアイテムタイプ_（フル）(1) | |||||||||
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| 公開日 | 2023-03-18 | |||||||||
| タイトル | ||||||||||
| タイトル | Topological Aspects of Classical and Quantum(2+1)-dimensional Gravity | |||||||||
| 言語 | en | |||||||||
| タイトル | ||||||||||
| タイトル | 古典及び量子(2+1)次元重力の位相的側面 | |||||||||
| 言語 | ja | |||||||||
| 作成者 |
早田, 次郎
× 早田, 次郎
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| アクセス権 | ||||||||||
| アクセス権 | open access | |||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
| 権利情報 | ||||||||||
| 権利情報 | Copyright(c) by Author | |||||||||
| 主題 | ||||||||||
| 主題Scheme | NDC | |||||||||
| 主題 | 420 | |||||||||
| 内容記述 | ||||||||||
| 内容記述 | In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g = 0 and g = 1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g = 1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace naoclel of (2+1)-dimensional gravity with the matter fields in the case of g = 0 and y = 1. For g = 0, a wormhole solution is found but for g = 1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g = 1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity. | |||||||||
| 言語 | en | |||||||||
| 内容記述 | ||||||||||
| 内容記述タイプ | TableOfContents | |||||||||
| 内容記述 | ABSTRACT / p3 CONTENTS / p4 1 Introduction / p5 2 ADM Canonical Formalism / p9 3 York's Formalism / p13 4 Evolution of the Geometry / p17 5 Phase Space Reduction / p23 6 Linearized Gravity / p27 7 Mini-superspace / p31 8 Quantum Gravity / p35 9 Conclusion / p44 Appendix A / p46 Appendix B / p48 Appendix C / p54 | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_db06 | |||||||||
| 資源タイプ | doctoral thesis | |||||||||
| 出版タイプ | ||||||||||
| 出版タイプ | NA | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_be7fb7dd8ff6fe43 | |||||||||
| ID登録 | ||||||||||
| ID登録 | 10.11501/2964193 | |||||||||
| ID登録タイプ | JaLC | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | references | |||||||||
| 関連名称 | ・A. Hosoya and J. Soda, Mod. Phys. Lett. A4 (1989) 2539, | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | references | |||||||||
| 関連名称 | ・J. Soda, to be published in Prog. Theor. Phys. Vol.83 No.4 (April), | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | references | |||||||||
| 関連名称 | ・Y. Fujiwara and J. Soda, to be published in Frog. Theor. Phys. Vol.83 No.4 (April). | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | references | |||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | http://dx.doi.org/10.1142/S0217732389002847 | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | references | |||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | http://dx.doi.org/10.1143/PTP.83.805 | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | references | |||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | http://dx.doi.org/10.1143/PTP.83.733 | |||||||||
| 開始ページ | ||||||||||
| 開始ページ | 1 | |||||||||
| 書誌情報 |
p. 1 |
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| 学位授与番号 | ||||||||||
| 学位授与番号 | 甲第831号 | |||||||||
| 学位名 | ||||||||||
| 言語 | ja | |||||||||
| 学位名 | 博士(理学) | |||||||||
| 学位名 | ||||||||||
| 言語 | en | |||||||||
| 学位名 | Physical Science | |||||||||
| 学位授与年月日 | ||||||||||
| 学位授与年月日 | 1990-03-26 | |||||||||
| 学位授与機関 | ||||||||||
| 学位授与機関識別子Scheme | kakenhi | |||||||||
| 学位授与機関識別子 | 15401 | |||||||||
| 言語 | ja | |||||||||
| 学位授与機関名 | 広島大学 | |||||||||
| 学位授与機関 | ||||||||||
| 言語 | en | |||||||||
| 学位授与機関名 | Hiroshima University | |||||||||
| 旧ID | 31751 | |||||||||
