  In eikonal and quenched approximation, it is argued that the strong coupling
fermionic QCD Green's functions and related amplitudes depart from a sole
dependence on the SUc(3) quadratic Casimir operator, C2f, evaluated over the
fundamental gauge group representation. Noticed in non-relativistic Quark
Models and in a non-perturbative generalization of the Schwinger mechanism, an
additional dependence on the cubic Casimir operator shows up, in
contradistinction with perturbation theory and other non-perturbative
approaches. However, it accounts for the full algebraic content of the rank-2
Lie algebra of SUc(3). Though numerically sub-leading effects, cubic Casimir
dependences, here and elsewhere, appear to be a signature of the
non-perturbative fermonic sector of QCD.
