物理学中的群论

grouptheoryprovidesthenaturalmathematicallanguagetoformulatesymmetryprinciplesandtoderivetheirconsequencesinmathematicsandinphysics.the"specialfunctions"ofmathematicalphysics，whichpervademathematicalanalysis,classicalphysics,andquantummechanics,invariablyoriginatefromunderlyingsymmetriesoftheproblemalthoughthetraditionalpresentationofsuchtopicsmaynotexpresslyemphasizethisuniversalfeature.moderndevelopmentsinallbranchesofphysicsareputtingmoreandmoreemphasisontheroleofsymmetriesoftheunderlyingphysicalsystems.thustheuseofgrouptheoryhasbecomeincreasinglyimportantinrecentyears.however,theincorporationofgrouptheoryintotheundergraduateorgraduatephysicscurriculumofmostuniversitieshasnotkeptupwiththisdevelopment.atbest,thissubjectisofferedasaspecialtopiccourse,cateringtoarestrictedclassofstudents.symptomaticofthisunfortunategapisthelackofsuitabletextbooksongeneralgroup-theoreticalmethodsinphysicsforallseriousstudentsofexperimentalandtheoreticalphysicsatthebeginninggraduateandadvancedundergraduatelevel.thisbookiswrittentomeetpreciselythisneed.therealreadyexist,ofcourse,manybooksongrouptheoryanditsapplicationsinphysics.foremostamongthesearetheoldclassicsbyweyl,wigner,andvanderwaerden.forapplicationstoatomicandmolecularphysics,andtocrystallatticesinsolidstateandchemicalphysics,therearemanyelementarytextbooksemphasizingpointgroups,spacegroups,andtherotationgroup.reflectingtheimportantroleplayedbygrouptheoryinmodernelementaryparticletheory,manycurrentbooksexpoundonthetheoryofliegroupsandliealgebraswithemphasissuitableforhighenergytheoreticalphysics.finally,thereareseveralusefulgeneraltextsongrouptheoryfeaturingcomprehensivenessandmathematicalrigorwrittenforthemoremathematicallyorientedaudience.experienceindicates,however,thatformoststudents,itisdifficulttofindasuitablemodernintroductorytextwhichisbothgeneralandreadilyunderstandable.