With the couplings between the eight gluons constrained by the structure constants of the su(3) algebra in QCD, one would expect that there should exist a special basis (or set of bases) for the algebra wherein, unlike in a Cartan-Weyl basis, all gluons interact identically (cyclically) with each other, explicitly on an equal footing. We report here particular such bases, which we have found in a computer search, and we indicate associated $3\times 3$ representations. We conjecture that essentially all cyclic bases for su(3) may be obtained from these making appropriate circulant transformations, and that cyclic bases may also exist for other $\mathrm{su}(n)$, $n>3$.

• Received 18 July 2013

DOI:https://doi.org/10.1103/PhysRevD.90.017502