作者	TheodoreFrankelFrankel
出版社
出版时间	2005-04-01

特色：

本书试图提供外微分形式、微分几何、代数拓扑、微分拓扑、李群、向量丛、Chern公式等前沿知识，它们对于深入理解经典物理、现代物理以及工程都是必需的。其中包含解析动力学、流体动力学、电磁学（在平坦空间和弯曲空间）、热力学、弹性理论、Kirchhoff电路定律的几何及拓扑、肥皂泡薄膜、狭义相对论和广义相对论、Dirac算子和旋量、Yang-Mills规范场、Aharonov-Bohm效应、Berry相、瞬子绕数、夸克、介子的夸克模型。在讨论抽象的微分几何概念前，通过大量的关于常规空间中曲面的研究培养几何直观，因此，学数学的学生对此书也会很干兴趣。本书对于物理、工程、数学的高年级学生和研究生是非常有益的，可供他们作为自学教材。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.