geometric algebra and its application to mathematical physics - c. doran

《geometric algebra and its application to mathematical physics - c. doran》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、GeometricAlgebraanditsApplicationtoMathematicalPhysicsChrisJ.L.DoranSidneySussexCollegeAdissertationsubmittedforthedegreeofDoctorofPhilosophyintheUniversityofCambridge.February1994PrefaceThisdissertationistheresultofworkcarriedoutintheDepartmentofAppliedMathe-maticsandThe

2、oreticalPhysicsbetweenOctober1990andOctober1993.Sectionsofthedissertationhaveappearedinaseriesofcollaborativepapers[1]

3、[10].Exceptwhereexplicitreferenceismadetotheworkofothers,theworkcontainedinthisdissertationismyown.AcknowledgementsManypeoplehavegivenhelpandsupportovert

4、helastthreeyearsandIamgratefultothemall.Ioweagreatdebttomysupervisor,NickManton,forallowingmethefreedomtopursuemyowninterests,andtomytwoprinciplecollaborators,AnthonyLasenbyandStephenGull,whoseideasandinspirationwereessentialinshapingmyresearch.IalsothankDavidHestenesforh

5、isencouragementandhiscompanyonanarduousjourneytoPoland.Aboveall,IthankJulieCookefortheloveandencouragementthatsustainedmethroughtothecompletionofthiswork.Finally,IthankStuartRankinandMargaretJamesformanyhappyhoursintheMill,MikeandRachael,TimandImogen,Paul,Alanandmyotherco

6、lleaguesinDAMTPandMRAO.IgratefullyacknowledgenancialsupportfromtheSERC,DAMTPandSidneySussexCollege.TomyparentsContents1Introduction11.1SomeHistoryandRecentDevelopments:::::::::::::::::::41.2AxiomsandDenitions:::::::::::::::::::::::::::::71.2.1TheGeometricProduct::::::::

7、::::::::::::::::111.2.2TheGeometricAlgebraofthePlane:::::::::::::::::121.2.3TheGeometricAlgebraofSpace::::::::::::::::::::151.2.4Re ectionsandRotations:::::::::::::::::::::::171.2.5TheGeometricAlgebraofSpacetime:::::::::::::::::211.3LinearAlgebra::::::::::::::::::::::::::

8、:::::::231.3.1LinearFunctionsandtheOutermorphism::::::::::::::231.3.2Non-OrthonormalFrames:::::::::::::::::::::::262GrassmannAlgebraandBerezinCalculus292.1GrassmannAlgebraversusCliordAlgebra::::::::::::::::::292.2TheGeometrisationofBerezinCalculus:::::::::::::::::::302.2

9、.1ExampleI.TheGrauss"Integral:::::::::::::::::::332.2.2ExampleII.TheGrassmannFourierTransform::