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group theory exceptional lie groups as invariance groups - p. cvitanovic

group theory exceptional lie groups as invariance groups - p. cvitanovic

ID：14375250

大小：1.70 MB

页数：168页

时间：2018-07-28

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1、printedApril14,2000CLASSICSILLUSTRATEDGROUPTHEORYExceptionalLiegroupsasinvariancegroupsPredragCvitanovi´cAbstractWeoffertheultimatebirdtrackerguidetoexceptionalLiegroups.Keywords:exceptionalLiegroups,invarianttheory,Titsmagicsquare—————————————————————-PRELIMINARYversionof30March2000ava

2、ilableon:www.nbi.dk/GroupTheory/p-cvitanovic@nwu.eduiiContents1Introduction12Apreview52.1Basicconcepts.............................52.2Firstexample:SU(n).........................92.3Secondexample:E6family......................123Invariantsandreducibility153.1Preliminaries..............

3、................153.1.1Groups.............................153.1.2Vectorspaces..........................163.1.3Algebra.............................173.1.4Definingspace,tensors,representations...........183.2Invariants................................203.2.1Algebraofinvariants.............

4、.........223.3Invariancegroups............................233.4Projectionoperators..........................243.5Furtherinvariants...........................253.6Birdtracks................................273.7Clebsch-Gordancoefficients......................293.8Zero-andone-dimensionalsub

5、spaces.................313.9Infinitesimaltransformations.....................323.10Liealgebra...............................363.11OtherformsofLiealgebracommutators...............383.12Irrelevancyofclebsches........................384Recouplings414.1Couplingsandrecouplings...............

6、........414.2Wigner3n−jcoefficients.......................444.3Wigner-Eckarttheorem........................455Permutations495.1Permutationsinbirdtracks......................495.2Symmetrization.............................50iiiivCONTENTS5.3Antisymmetrization..........................525.4

7、Levi-Civitatensor...........................535.5Determinants..............................555.6Characteristicequations........................575.7Fully(anti)symmetrictensors.....................575.8Youngtableaux,Dynkinlabels....................586Casimiroperators596.1CasimirsandLi

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