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Useful relations among the generators in the defining and adjoint representations of SU(N)

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arxiv 1912.13302 v2 pith:5HOGS2WO submitted 2019-12-31 math-ph hep-phmath.MP

Howard E. Haber This is my paper · ORCID
classification math-phhep-phmath.MP
keywords relationsadjointdefininggeneratorsrepresentationrepresentationsusefulalgebra
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc. Due to the existence of the completely symmetric tensor $d_{abc}$ that arises in the study of the SU(N) Lie algebra, one can also consider relations that involve the adjoint representation matrix, $(D^a)_{bc}=d_{abc}$. In this review, we summarize many useful relations satisfied by the defining and adjoint representation matrices of SU(N). A few relations special to the case of N=3 are highlighted.

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