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Dirac Laplacian . . . . . . . . . . . . . . . . . . . . . . 11\n\n2 Getzler’s RescalingTransformation 12\n 2.1 Review of Getzler’s RescalingTransformation . . . . . . . . . . . . . . . . . . . . . . . . . . 13\n 2.2 Rescaling of the Dirac Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15\n 2.3 Rescaling of the Heat Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16\n 2.4 Mehler’s formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22\n\n3 On the coefficients Kℓ,[p](P⁰) forℓ \u003e p/2 23 \n 3.1 Taylor expansion ofD(ε) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23\n 3.2 Main Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29\n\n4 Some computations 33\n 4.1 K₀(P⁰), K₁(P⁰), K₂(P⁰) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33\n\n5 Appendix 39\n 5.1 Index Theorem for the Dirac Operator . . . 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A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds
https://doi.org/10.24561/00019663
https://doi.org/10.24561/000196637efbf0cf-cd83-4b3d-87c1-294942414680
名前 / ファイル | ライセンス | アクション |
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GD0001350.pdf (356.9 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||||||
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公開日 | 2022-10-07 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds | |||||||||
言語 | ||||||||||
言語 | jpn | |||||||||
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 | |||||||||
ID登録 | ||||||||||
ID登録 | 10.24561/00019663 | |||||||||
ID登録タイプ | JaLC | |||||||||
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 | |||||||||
タイトル(別言語) | ||||||||||
その他のタイトル | スピン多様体上のディラックラプラシアンの熱核係数公式 | |||||||||
著者 |
白川, 匠
× 白川, 匠
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著者 所属 | ||||||||||
埼玉大学大学院理工学研究科(博士後期課程)理工学専攻 | ||||||||||
著者 所属(別言語) | ||||||||||
Graduate School of Science and Engineering, Saitama University | ||||||||||
書誌 | ||||||||||
収録物名 | 博士論文(埼玉大学大学院理工学研究科(博士後期課程)) | |||||||||
書誌情報 |
発行日 2021 |
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出版者名 | ||||||||||
出版者 | 埼玉大学大学院理工学研究科 | |||||||||
出版者名(別言語) | ||||||||||
出版者 | Graduate School of Science and Engineering, Saitama University | |||||||||
形態 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | 42p | |||||||||
学位授与番号 | ||||||||||
学位授与番号 | 甲第1220号 | |||||||||
学位授与年月日 | ||||||||||
学位授与年月日 | 2021-09-22 | |||||||||
学位名 | ||||||||||
学位名 | 博士(理学) | |||||||||
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 | 12401 | |||||||||
学位授与機関名 | 埼玉大学 | |||||||||
目次 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | 0 Introduction 2 1 Preliminary 3 1.1 Spin group and Clifford algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Spinor representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Spin manifolds and the Dirac operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Heat equation associated with the Dirac Laplacian . . . . . . . . . . . . . . . . . . . . . . 11 2 Getzler’s RescalingTransformation 12 2.1 Review of Getzler’s RescalingTransformation . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Rescaling of the Dirac Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Rescaling of the Heat Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Mehler’s formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 On the coefficients Kℓ,[p](P⁰) forℓ > p/2 23 3.1 Taylor expansion ofD(ε) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Main Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Some computations 33 4.1 K₀(P⁰), K₁(P⁰), K₂(P⁰) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5 Appendix 39 5.1 Index Theorem for the Dirac Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 |
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注記 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | 指導教員 : 下川航也 | |||||||||
版 | ||||||||||
[出版社版] | ||||||||||
著者版フラグ | ||||||||||
出版タイプ | VoR | |||||||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||
資源タイプ | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | text | |||||||||
フォーマット | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | application/pdf | |||||||||
作成日 | ||||||||||
日付 | 2022-10-07 | |||||||||
日付タイプ | Created | |||||||||
アイテムID | ||||||||||
GD0001350 |