出版社：世界图书出版公司北京公司
年代：2009
定价：49.0
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。
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
Thisbook,whichbeganasaseminarin1985atMIT,containscompleteproofsofthelocalindextheoremforDiracoperatorsusingtheheatkernelapproach,togetherwithitsgeneralizationstoequivariantDiracoperatorsandfamiliesofDiracoperators,aswellasbackgroundmaterialonsuperconnectionsandequivariantdifferentialforms.
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| 书名 | 热核与狄拉克算子站内查询相似图书 | ||
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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 | |
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。