热核与狄拉克算子

(法) 波林, 著

出版社：世界图书出版公司北京公司

年代：2009

定价：49.0

书籍简介:

本书作者用生动的语言介绍深奥的理论，书中前四章可作为研究生课程“线性椭圆算子在微分几何中的应用”使用，基础微分几何是唯一需要熟悉的基础知识。接下来的四章讨论等变指标定理，包括对等变微分形式一个有用的介绍。最后两章是本书的精华所在，给出了Dirac算子Bismut局部族指标定理的证明。

书籍目录:

Introduction

IBackgroundonDifferentialGeometry

1.IFibreBundlesandConnections

1.2RiemannianManifolds

1.3Superspaces

1.4Superconnections

1.5CharacteristicClasses

1.6TheEulerandThornClasses

2AsymptoticExpansionoftheHeatKernel

2.1DifferentialOperators

2.2TheHeatKernelonEuclideanSpace

2.3HeatKernels

2.4ConstructionoftheHeatKernel

2.5TheFormalSolution

2.6TheTraceoftheHeatKernel

2.7HeatKernelsDependingonaParameter

3CliffordModulesandDiracOperators

3.1TheCliffordAlgebra

3.2Spinors

3.3DiracOperators

3.4IndexofDiracOperators

3.5TheLichnerowiczFormula

3.6SomeExamplesofCliffordModules

4IndexDensityofDiracOperators

4.1TheLocalIndexTheorem

4.2MehlersFormula

4.3CalculationoftheIndexDensity

5TheExponentialMapandtheIndexDensity

5.1JacobianoftheExponentialMaponPrincipalBundles

5.2TheHeatKernelofaPrincipalBundle

5.3CalculuswithGrassmannandCliffordVariables

5.4TheIndexofDiracOperators

6TheEquivariantIndexTheorem

6.1TheEquivariantIndexofDiracOperators

6.2TheAtiyah-BottFixedPointFormula

6.3AsymptoticExpansionoftheEquivariantHeatKernel

6.4TheLocalEquivariantIndexTheorem

6.5GeodesicDistanceonaPrincipalBundle

6.6Theheatkernelofanequivariantvectorbundle

6.7ProofofProposition6.13

7EquivariantDifferentialForms

7.1EquivariantCharacteristicClasses

7.2TheLocalizationFormula

7.3BottsFormulasforCharacteristicNumbers

7.4ExactStationaryPhaseApproximation

7.5TheFourierTransformofCoadjointOrbits

7.6EquivariantCohomologyandFamilies

7.7TheBottClass

8TheKiriliovFormulafortheEquivariantIndex

8.1TheKirillovFormula

8.2TheWeylandKirillovCharacterFormulas

8.3TheHeatKernelProofoftheKirillovFormula

9TheIndexBundle

9.lTheIndexBundleinFiniteDimensions

9.2TheIndexBundleofaFamilyofDiracOperators

9.3TheChernCharacteroftheIndexBundle

9.4TheEquivariantIndexandtheIndexBundle

9.5TheCaseofVaryingDimension

9.6TheZeta-FunctionofaLaplaeian

9.7TheDeterminantLineBundle

10TheFamilyIndexTheorem

10.1RiemannianFibreBundles

10.2CliffordModulesonFibreBundles

10.3TheBismutSuperconnection

10.4TheFamilyIndexDensity

10.5TheTransgressionFormula

10.6TheCurvatureoftheDeterminantLineBundle

10.7TheKirillovFormulaandBismutsIndexTheorem

References

ListofNotation

Index

内容摘要:

　　Thisbook,whichbeganasaseminarin1985atMIT,containscompleteproofsofthelocalindextheoremforDiracoperatorsusingtheheatkernelapproach,togetherwithitsgeneralizationstoequivariantDiracoperatorsandfamiliesofDiracoperators,aswellasbackgroundmaterialonsuperconnectionsandequivariantdifferentialforms.

书籍规格:

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出版地	北京	出版单位	世界图书出版公司北京公司
版次	1版	印次	1
定价(元)	49.0	语种	英文
尺寸	14	装帧	平装
页数		印数	1000

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书籍信息归属:

热核与狄拉克算子是世界图书出版公司北京公司于2009.08出版的中图分类号为 O175.3 的主题关于微分算子－英文的书籍。