物理学家的几何学

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。