《物理学家的几何学》(The Geometry of Physics)文字第三版

这本书最伟大的价值从第三部分开始展现. 非常有趣. 值得花时间啃. 当然,要研读这有趣的部分,微分几何的基础是要稍微有了解的,这就是此书的第一部分和第二部分的主要内容了

TheGeometryofPhysics
Thisbookisintendedtoprovideaworkingknowledgeofthosepartsofexteriordifferential
forms,differentialgeometry,algebraicanddifferentialtopology,Liegroups,vectorbundles,
andChernformsthatareessentialforadeeperunderstandingofbothclassicalandmodern
physicsandengineering.Includedarediscussionsofanalyticalandfluiddynamics,elec-
tromagnetism(inflatandcurvedspace),thermodynamics,elasticitytheory,thegeometry
andtopologyofKirchhoff’selectriccircuitlaws,soapfilms,specialandgeneralrelativity,
theDiracoperatorandspinors,andgaugefields,includingYang–Mills,theAharonov–
Bohmeffect,Berryphase,andinstantonwindingnumbers,quarks,andthequarkmodelfor
mesons.Beforeadiscussionofabstractnotionsofdifferentialgeometry,geometricintuition
isdevelopedthrougharatherextensiveintroductiontothestudyofsurfacesinordinary
space;consequently,thebookshouldbeofinterestalsotomathematicsstudents.
Thisbookwillbeusefultograduateandadvanceundergraduatestudentsofphysics,
engineering,andmathematics.Itcanbeusedasacoursetextorforself-study.
ThisThirdEditionincludesanewoverviewofCartan’sexteriordifferentialforms.It
previewsmanyofthegeometricconceptsdevelopedinthetextandillustratestheirappli-
cationstoasingleextendedprobleminengineering;namely,theCauchystressescreated
byasmalltwistofanelasticcylindricalrodaboutitsaxis.
TheodoreFrankelreceivedhisPh.D.fromtheUniversityofCalifornia,Berkeley.Heis
currentlyEmeritusProfessorofMathematicsattheUniversityofCalifornia,SanDiego.
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