热核与狄拉克算子(英文版)
¥
175
九品
库存2件
作者波林 著
出版社世界图书出版公司
出版时间2009-08
版次1
装帧平装
货号B1654
上书时间2024-07-26
商品详情
- 品相描述:九品
图书标准信息
-
作者
波林 著
-
出版社
世界图书出版公司
-
出版时间
2009-08
-
版次
1
-
ISBN
9787506292139
-
定价
49.00元
-
装帧
平装
-
开本
24开
-
纸张
其他
-
页数
363页
-
正文语种
英语
- 【内容简介】
-
Thisbook,whichbeganasaseminarin1985atMIT,containscompleteproofsofthelocalindextheoremforDiracoperatorsusingtheheatkernelapproach,togetherwithitsgeneralizationstoequivariantDiracoperatorsandfamiliesofDiracoperators,aswellasbackgroundmaterialonsuperconnectionsandequivariantdifferentialforms.
Sincethepublicationofthefirstedition,thesubjectstreatedherehavecontin-uedtofindnewapplications.Equivariantcohomologyplaysanimportantroleinthestudyofsymplecticreduction,andBismutsuperconnectionsandthelocalindexthe-oremforfamilieshavehadmanyapplications,throughtheconstructionofhigheranalytictorsionformsandcurrents.(Forasurveyofsomeofthesedevelopments,werecommendreadingBismutstalkattheBerlinInternationalCongressofMathe-maticians,reference
Althoughthisbooklackssomeoftheusualattributesofatextbook(suchasexercises),ithasbeenwidelyusedinadvancedcoursesindifferentialgeometry;formanyofthetopicsdiscussedhere,therearenoothertreatmentsavailableinmonographform.Becauseofthecontinuingdemandfromstudentsforthebook,wewerevery
- 【目录】
-
Introduction
1BackgroundonDifferentialGeometry
1.1FibreBundlesandConnections
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
3CLiffordModulesandDiraeOperators
3.1TheCliffordAlgebra
3.2Spinors
3.3DiracOperators
3.4IndexofDiracOperators
3.5TheLichnerowiczFormula
3.6SomeExamplesofCliffordModules
4IndexDensityofDiracOperators
4.1TheLocalIndexTheorem
4.2MehlersFormula
4.3CalculationoftheIndexDensity
5TheExponentialMapandtheIndexDensity
5,1IacobianoftheExponentialMaponPrincipalBundles
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
5TheFourierTransformofCoadjointOrbits
7.6EquivariantCohomologyandFamilies
7.7TheBottClass
8TheKirillovFormulafortheEquivariantIndex
8.1TheKirillovFormula
8.2TheWeylandKirillovCharacterFormulas
8.3TheHeatKernelProofoftheKirillovFormula
9TheIndexBundle
9.1TheIndexBundleinFiniteDimensions
9.2TheIndexBundleofaFamilyofDiracOperators
9.3TheChernCharacteroftheIndexBundle
9.4TheEquivariantIndexandtheIndexBundle
9.5TheCaseofVaryingDimension
9.6TheZeta-FunctionofaLaplacian
9.7TheDeterminantLineBundle
10TheFamilyIndexTheorem
10.1RiemannianFibreBundles
10.2CliffordModulesonFibreBundles
10.3TheBismutSuperconnection
10.4TheFamilyIndexDensity
10.5TheTransgressionFormula
10.6TheCurvatureoftheDeterminantLineBundle
10.7TheKirillovFormulaandBismutsIndexTheorem
点击展开
点击收起
— 没有更多了 —
以下为对购买帮助不大的评价