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1、TheconceptualoriginsofMaxwell’sequationsandgaugetheoryChenNingYangAlreadyinFaraday’selectrotonicstateandMaxwell’svectorpotential,gaugefreedomwasanunavoidablepresence.Convertingthatpresencetothesymmetryprinciplethatunderpinsoursuccessfulstandardmodelisastoryworthtelling.ItisoftensaidthatafterCharles
2、AugustindeCoulomb,CarlFriedrichGauss,AndréMarieAmpère,andMichaelFaradaydiscoveredthefourexperimentallawsconcerningelectricityandmagnetism,JamesClerkMaxwelladdedthedisplacementcurrentandtherebycreatedthegreatsetofMaxwell’sequations.Thatviewisnotentirelywrong,butitobscuresthesubtleinterplaybetweensop
3、histicatedgeometricalandphysicalintuitionsthatlednotonlytothereplacementof“actionatadistance”byfieldtheoryinthe19thcenturybutalso,inthe20thcentury,totheverysuccessfulstandardmodelofparticlephysics.The19thcenturyIn1820HansChristianOersted(1777–1851)discoveredthatanelectriccurrentwouldalwayscausemagn
4、eticneedlesinitsneighborhoodtomove.ThediscoveryelectrifiedthewholeofEuropeandledtothesuccessfulmathematicaltheoryof“actionatadistance”byAmpère(1775–1836).InEngland,Faraday(1791–1867)wasalsogreatlyexcitedbyOersted’sdiscovery.ButhelackedthemathematicaltrainingneededtounderstandAmpère.InalettertoAmpèr
5、edated3September1822,Faradaylamented,“Iamunfortunateinawantofmathematicalknowledgeandthepowerofenteringwithfacilityintoabstractreasoning.Iamobligedtofeelmywaybyfactscloselyplacedtogether.”1Faraday’s“facts”werehisexperiments,bothpublishedandunpublished.Duringaperiodof23years,1831–54,hecompiledtheres
6、ultsofthoseexperimentsintothreevolumes,calledExperimentalResearchesinElectricity,whichweshallrefertoasER(figure1).Amostremarkablethingisthattherewasnotasingleformulainthismonumentalcompilation,whichshowedthatFaradaywasfeelinghisway,guidedonlybygeometricintuitionwithoutanyprecisealgebraicformulation
7、.Figure1.ThreevolumesofFaraday’sExperimentalResearchesinElectricity,publishedseparatelyin1839,1844,and1855.Ontherightisthefirstpageofthefirstvolume.STEFANKABEN,NIELSBOHRLIBRARYANDESVAFigure2showsadiagramfro
