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1、NadirJeevanjeeAnIntroductiontoTensorsandGroupTheoryforPhysicistsPrefaceThisbookiscomposedoftwoparts:PartI(Chaps.1through3)isanintroductiontotensorsandtheirphysicalapplications,andPartII(Chaps.4through6)introducesgrouptheoryandintertwinesitwiththeearliermaterial.Bothpart
2、sarewrittenattheadvanced-undergraduate/beginning-graduatelevel,althoughinthecourseofPartIIthesophisticationlevelrisessomewhat.Thoughthetwopartsdiffersomewhatinflavor,Ihaveaimedinbothtofilla(perceived)gapintheliteraturebyconnectingthecomponentformalismsprevalentinphysicsca
3、lculationstotheabstractbutmoreconceptualformulationsfoundinthemathliterature.Myfirmbeliefisthatweneedtoseetensorsandgroupsincoordinatestogetasenseofhowtheywork,butalsoneedanabstractformulationtounderstandtheiressentialnatureandorganizeourthinkingaboutthem.Myoriginalmotiv
4、ationforthebookwastodemystifytensorsandprovideauni-fiedframeworkforunderstandingtheminallthedifferentcontextsinwhichtheyariseinphysics.Thewordtensorisubiquitousinphysics(stresstensor,moment-of-inertiatensor,fieldtensor,metrictensor,tensorproduct,etc.)andyettensorsarerarel
5、ydefinedcarefully,andthedefinitionusuallyhastodowithtransformationproperties,makingitdifficulttogetafeelforwhattheseobjectsare.Furthermore,physicstextsatthebeginninggraduatelevelusuallyonlydealwithtensorsintheircomponentform,sostudentswonderwhatthedifferenceisbetweenasecon
6、dranktensorandamatrix,andwhynew,enigmaticterminologyisintroducedforsome-thingtheyhavealreadyseen.Allofthisproducesalingeringunease,whichIbelievecanbealleviatedbyformulatingtensorsinamoreabstractbutconceptuallymuchclearerway.Thiscoordinate-freeformulationisstandardinthem
7、athematicalliter-atureondifferentialgeometryandinphysicstextsonGeneralRelativity,butasfarasIcantellisnotaccessibletoundergraduatesorbeginninggraduatestudentsinphysicswhojustwanttolearnwhatatensoriswithoutdealingwiththefullma-chineryoftensoranalysisonmanifolds.Theironyof
8、thissituationisthataproperunderstandingoftensorsdoesnotrequiremuchmoremathematicsthanwhatyoulikelyencountereda
