物理学家的几何学

图书标准信息

• 作者 [美]弗兰克尔 著
• 出版社 清华大学出版社
• 出版时间 2005-04
• 版次 2
• ISBN 9787302073512
• 定价 84.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 694页
• 丛书 天元基金影印系列丛书

【内容简介】

Thisbookisintendedtoprovideaworkingknowledgeofthosepartsofexteriordifferentialforms，differentialgeometry，algebraicanddifferentialtopology，Liegroups，vectorbundles，andChernformsthatareessentialforadeeperunderstandingofbothclassicalandmodernphysicsandengineering。Includedarediscussionsofanalyticalandfluiddynamics，electromagnetism（inflatandcurvedspace），thermodynamics，elasticitytheory，thegeometryandtopologyofKirchhoff’selectriccircuitlaws，soapfilms，specialandgeneralrelativity，theDiracoperatorandspinors，andgaugefields，includingYang-Mills，theAharonov-Bohmeffect，Berryphase，andinstantonwindingnumbers，quarks，andthequarkmodelformesons。Beforeadiscussionofabstractnotionsofdifferentialgeometry，geometricintuitionisdevelopedthrougharatherextensiveintroductiontothestudyofsurfacesinordinaryspace；consequently，thebookshouldbeofinterestalsotomathematicsstudents。
Thisbookwillbeusefultograduateandadvancedundergraduatestudentsofphysics，engineering，andmathematics。Itcanbeusedasacoursetextofforself-study。
Thissecondeditionincludesthreenewappendices，AppendixC，Symmetries，Quarks，andMesonMasses（whichconcludeswiththefamousGell-Mann/Okubomassformula）；AppendixD，RepresentationsandHyperelasticBodies；andAppendixE，OrbitsandMorse-BottTheoryinCompactLieGroups。BothAppendixCandDinvolveresultsfromthetheoryofrepresentationsofcompactLiegroups，whicharedevelopedhere。AppendixEdelvesdeeperintothegeometryandtopologyofcompactLiegroups。

【目录】

PrefacetotheSecondEdition
PerfacetotheRevisedPrinting
PerfacetotheFirstEdition
ⅠManifolds,Tensors,andExteriorForms
1ManifoldsandVectorFields
2TensorsandExteriorForms
3IntegrationofDifferentialForms
4TheLieDerivative
5ThePoincaréLemmaandPotentials
6HolonomicandNonholonomicConstraints
ⅡGeometryandTopology
7R3andMinkowskiSpace
8TheGeometryofSurfacesinR3
9CovariantDifferentiationandCurvature
10Geodesics
11Relativity,Tensors,andCurvature
12CurvatureandTopology:Synge’sTheorem
13BettiNumbersandDeRham’sTheorem
14HarmonicForms
ⅢLieGroups,Bundles,andChernForms
15LieGroups
16VectorBundlesinGeometryandPhysics
17FiberBundles,Gauss\|Bonnet,andTopologicalQuantization
18ConnectionsandAssociatedBundles
19TheDiracEquation
20Yang\|MillsFields
21BettiNumbersandCoveringSpaces
22ChernFormsandHomotopyGroups