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1、Chapter1IntroductionAsfarasIcansee,allaprioristatementsinphysicshavetheirorigininsymmetry.
2、HermannWeyl11.1SymmetryinPhysicsSymmetryisafundamentalhumanconcern,asevidencedbyitspres-enceintheartifactsofvirtuallyallcultures.Symmetricobjectsareaestheticallyappealingtothehumanmindand,in
3、fact,theGreekworksymmetroswasmeantoriginallytoconveythenotionofwell-proportioned"orarmonious."Thisfascinationwithsymmetry¯rstfounditsrationalexpressionaround400B.C.inthePlatonicsolidsandcontinuestothisdayunabatedinmanybranchesofscience.1.1.1WhatisaSymmetry?Anobjectissaidtobesymme
4、tric,ortohaveasymmetry,ifthereisatransformation,suchasarotationorre°ection,wherebytheobjectlooksthesameafterthetransformationasitdidbeforethetransforma-tion.InFig.1.3,weshowanequilateraltriangle,asquare,andacircle.Thetriangleisindistinguishableafterrotationsof1¼and2¼around33itsgeo
5、metriccenter,orsymmetryaxis.Thesquareisindistinguishable1InSymmetry(PrincetonUniversityPress,1952)12Introductionafterrotationsof1¼,¼,and3¼,andthecircleisindistinguishableafter22allrotationsaroundtheirsymmetryaxes.Thesetransformationsaresaidtobesymmetrytransformationsofthecorrespon
6、dingobject,whicharesaidtobeinvariantundersuchtransformations.Themoresymme-trytransformationsthatanobjectadmits,themoreymmetric"itissaidtobe.Onethisbasis,thecircleisoresymmetric"thanthesquarewhich,inturn,ismoresymmetricthanthetriangle.Anotherpropertyofthesymmetrytransformationsofth
7、eobjectsinFig.1.3thatiscentraltothiscourseisthatthoseforthetriangleandsquarearediscrete,i.e.,therotationangleshaveonlydiscretevalues,whilethoseforthecirclearecontinuous.(a)(b)(c)Figure1.1:Anequilateraltriangle(a),square(b)andcircle(c).Theseob-jectsareinvarianttoparticularrotations
8、aboutaxesthatareperpendiculartotheirplaneandpassthroughtheirgeometriccenters(indicatedbydots).1.1.2SymmetryinPhysicalLawsInthephysicalsciences,symmetryisoffundamentalbecausetherearetransformationswhichleavethelawsofphysicsinvariant.Suchtrans-formationsinvolvechangingthevariableswi
9、thinaphysicallawsuchthattheequati
