@phdthesis{oai:sucra.repo.nii.ac.jp:00019694,
 author = {白川, 匠},
 month = {},
 note = {42p, 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, 指導教員 : 下川航也, text, application/pdf},
 school = {埼玉大学},
 title = {A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds},
 year = {2021},
 yomi = {シラカワ, タクミ}
}