A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds

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DOI[10.24561/00019663]to the data of the same series

A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds

Persistent ID (NDL): info:ndljp/pid/12508587

Material type: 博士論文

Author: 白川, 匠

Publisher: 埼玉大学大学院理工学研究科

Publication date: 2021

Material Format: Digital

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Name of awarding university/degree: 埼玉大学,博士(理学)

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Note (General)：: type:text0 Introduction 21 Preliminary 3 1.1 Spin group and Clifford algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2...

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Material Type: 博士論文
Title: A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds
Author/Editor: 白川, 匠
Author Heading: 白川, 匠
Publication, Distribution, etc.: 埼玉大学大学院理工学研究科
Publication Date: 2021
Publication Date (W3CDTF): 2021
Alternative Title: 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
Degree grantor/type: 埼玉大学
Date Granted: 2021-09-22
Date Granted (W3CDTF): 2021-09-22
Dissertation Number: 甲第1220号
Degree Type: 博士(理学)
Text Language Code: jpn
Target Audience: 一般
Note (General): type:text
0 Introduction 21 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 . . . . . . . . . . . . . . . . . . . . . . 112 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 On the coefficients Kℓ,[p](P⁰) forℓ > p/2 23 3.1 Taylor expansion ofD(ε) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Main Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Some computations 33 4.1 K₀(P⁰), K₁(P⁰), K₂(P⁰) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Appendix 39 5.1 Index Theorem for the Dirac Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
指導教員 : 下川航也
DOI: 10.24561/00019663
https://doi.org/10.24561/00019663
Persistent ID (NDL): info:ndljp/pid/12508587
https://dl.ndl.go.jp/pid/12508587
Collection: 障害者向け資料
Collection (Materials For Handicapped People:1): テキストデータ
Collection (particular): 国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文
https://dl.ndl.go.jp/collections/A00014
Acquisition Basis: 博士論文（自動収集）
Date Accepted (W3CDTF): 2023-01-30T13:49:32+09:00
Format (IMT): application/pdf
Access Restrictions: 国立国会図書館内限定公開
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Periodical Title (URI): https://doi.org/10.24561/00019663
http://id.nii.ac.jp/1586/00019663/
Data Provider (Database): 国立国会図書館 : 国立国会図書館デジタルコレクション
https://dl.ndl.go.jp