{"created":"2023-05-15T15:29:50.247199+00:00","id":19694,"links":{},"metadata":{"_buckets":{"deposit":"11ab342c-c5fa-43ff-8eda-321e75fb0f0c"},"_deposit":{"created_by":15,"id":"19694","owners":[15],"pid":{"revision_id":0,"type":"depid","value":"19694"},"status":"published"},"_oai":{"id":"oai:sucra.repo.nii.ac.jp:00019694","sets":["94:429:431:432:1028"]},"author_link":[],"item_113_alternative_title_1":{"attribute_name":"タイトル（別言語）","attribute_value_mlt":[{"subitem_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"}]},"item_113_biblio_info_9":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2021","bibliographicIssueDateType":"Issued"}}]},"item_113_date_35":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2022-10-07","subitem_date_issued_type":"Created"}]},"item_113_date_granted_20":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2021-09-22"}]},"item_113_degree_grantor_22":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"埼玉大学"}],"subitem_degreegrantor_identifier":[{"subitem_degreegrantor_identifier_name":"12401","subitem_degreegrantor_identifier_scheme":"kakenhi"}]}]},"item_113_degree_name_21":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士(理学)"}]},"item_113_description_13":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_description":"42p","subitem_description_type":"Other"}]},"item_113_description_24":{"attribute_name":"目次","attribute_value_mlt":[{"subitem_description":"0 Introduction 2\n\n1 Preliminary 3\n 1.1 Spin group and Clifford algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3\n 1.2 Spinor representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5\n 1.3 Spin manifolds and the Dirac operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8\n 1.4 Heat equation associated with the 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 > 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39","subitem_description_type":"Other"}]},"item_113_description_25":{"attribute_name":"注記","attribute_value_mlt":[{"subitem_description":"指導教員 : 下川航也","subitem_description_type":"Other"}]},"item_113_description_33":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_type":"Other"}]},"item_113_description_34":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_113_dissertation_number_19":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲第1220号"}]},"item_113_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24561/00019663","subitem_identifier_reg_type":"JaLC"}]},"item_113_publisher_11":{"attribute_name":"出版者名","attribute_value_mlt":[{"subitem_publisher":"埼玉大学大学院理工学研究科"}]},"item_113_publisher_12":{"attribute_name":"出版者名（別言語）","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Science and Engineering, Saitama 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