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

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.

11 pages, a collection of useful formulae from a variety of sources; version 2 matches the published version

References in corpus (1)

• The LPM effect in sequential bremsstrahlung: from large-N QCD to N=3 via the SU(N) analog of Wigner 6-j symbols

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