Geometry of the Diric theory

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1、In:ASymposiumontheMathematicsofPhysicalSpace-Time,FacultaddeQuimica,UniversidadNacionalAutonomadeMexico,MexicoCity,67{96,(1981).GEOMETRYOFTHEDIRACTHEORYDavidHestenesABSTRACT.TheDiracwavefunctionisrepresentedinaformwhereallitscomponentshaveobviousgeometricalandphys

2、icalinterpretations.SixcomponentscomposeaLorentztransformationdeterminingtheelectronvelocityarespindirections.Thisprovidesthebasisforarigorousconnec-tionbetweenrelativisticrigidbodydynamicsandthetimeevolutionofthewavefunction.Thescatteringmatrixisgivenanewformasas

3、pinor-valuedoperatorratherthanacomplexfunction.Theapproachrevealsageomet-ricstructureofthescatteringmatrixandsimpli¯esscatteringcalculations.Thisclaimissupportedbyanexplicitcalculationofthedi®erentialcross-sectionandpolarizationchangeinCoulombscattering.Implicatio

4、nsforthestructureandinterpretationofrelativisticquantumtheoryarediscussed.INTRODUCTIONTheDiracequationisoneofthemostwell-establishedequationsofphysics,havingledtoagreatvarietyofdetailedpredictionswhichhavebeenexperimentallycon¯rmedwithhighprecision.Yettherelativis

5、ticquantumtheorybasedontheDiracequationhasneverbeengivenasinglecompleteandselfconsistentphysicalinterpretationwhichallphysicists¯ndsatisfactory.Moreover,itisgenerallyagreedthatthetheorymustbemodi¯edtoaccountfortheelectronmass,butthereishardlyagreementonhowtogoabou

6、tit.Thispaperreviewsandextendsresultsfromalineofresearch(Ref.[1{7])aimedatclarifyingtheDiractheoryandsimplifyingitsmathematicalformulation.Ofcourse,anysuchimprovementinsousefulatheorywouldbevaluableinitself.Buttheultimategoalistoachieveinsightintothestructureofthe

7、theorywhichidenti¯esthosefeaturesresponsibleforitsamazingresults,aswellasfeatureswhichmightbemodi¯edtoimproveit.ThecentralresultofthisresearchisaformulationoftheDiracspinorwavefunctionwhichrevealsthegeometricalandphysicalinterpretationofallitscomponents.Thismakesi

8、tpossibletorelatethetimeevolutionofthewavefunctiontorelativisticrigidbodymechanics,thusgivinginsightintothedynamicsandestablishingaconnectionwithclassic