Lie Groups, Lie Algebras & Some of Their Applications

Liegrouptheoryplaysanincreasinglyimportantroleinmodernphysicaltheories.Manyofitscalculationsremainfundamentallyunchangedfromonefieldofphysicstoanother,alteringonlyintermsofsymbolsandthelanguage.UsingthetheoryofLiegroupsasaunifyingvehicle,conceptsandresultsfromseveralfieldsofphysicscanbeexpressedinanextremelyeconomicalway.Withrigorandclarity,thistextintroducesupper-levelundergraduatestudentstoLiegrouptheoryanditsphysicalapplications.Anopeningdiscussionofintroductoryconceptsleadstoexplorationsoftheclassicalgroups,continuousgroupsandLiegroups,andLiegroupsandLiealgebras.Somesimplebutilluminatingexamplesarefollowedbyexaminationsofclassicalalgebras,Liealgebrasandrootspaces,rootspacesandDynkindiagrams,realforms,andcontractionsandexpansions.Reinforcedbynumerousexercises,solvedproblems,andfigures,thetextconcludeswithabibliographyandindexes.