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1、PatrickR.GirardQuaternions,CliffordAlgebrasandRelativisticPhysicsBirkhäuserBasel.Boston.BerlinAuthor:PatrickR.GirardIgorYa.SubbotinINSAdeLyonDepartmentofMathematicsandNaturalSciencesDépartementPremierCycleNationalUniversity20,avenueAlbertEinsteinLosAngelesCampu
2、sF-69621VilleurbanneCedex5245Paci¿cConcourseDriveFranceLosAngeles,CA90045e-mail:patrick.girard@insa-lyon.frUSAe-mail:isubboti@nu.edu2000MathematicalSubjectClassification:15A66,20G20,30G35,35Q75,78A25,83A05,83C05,83C10LibraryofCongressControlNumber:2006939566Bibl
3、iographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographicdataisavailableintheInternetat.ISBN978-3-7643-7790-8BirkhäuserVerlagAG,Basel–Boston–BerlinThisw
4、orkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broad-casting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Foranykindofuseperm
5、issionofthecopyrightownermustbeobtained.OriginallypublishedinFrenchunderthetitle“Quaternions,algèbredeCliffordetphysiquerelativiste”.©2004Pressespolytechniquesetuniversitairesromandes,LausanneAllrightsreserved©2007BirkhäuserVerlagAG,P.O.Box133,CH-4010Basel,Swit
6、zerlandPartofSpringerScience+BusinessMediaPrintedonacid-freepaperproducedfromchlorine-freepulp.TCFÑÑPrintedinGermanyISBN-10:3-7643-7790-8e-ISBN-10:3-7643-7791-7ISBN-13:978-3-7643-7790-8e-ISBN-13:978-3-7643-7791-5987654321www.birkhauser.chToIsabelle,mywife,andto
7、ourchildren:Claire,B´eatrice,ThomasandBenoˆıtForewordTheuseofCliffordalgebrainmathematicalphysicsandengineeringhasgrownrapidlyinrecentyears.Cliffordhadshownin1878theequivalenceoftwoap-proachestoCliffordalgebras:ageometricalonebasedontheworkofGrassmannandanalgebrai
8、coneusingtensorproductsofquaternionalgebrasH.Recentde-velopmentshavefavoredthegeometricapproach(geometricalgebra)leadingtoanalgebra(space-timealgebra)complexifiedbythealgebra
