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.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.13302
 Bibcode:
 2019arXiv191213302H
 Keywords:

 Mathematical Physics;
 High Energy Physics  Phenomenology
 EPrint:
 11 pages, a collection of useful formulae from a variety of sources