Casimir operator dependences of nonperturbative fermionic QCD amplitudes

Abstract

In eikonal and quenched approximations, it is argued that the strong coupling fermionic QCD Green’s functions and related amplitudes depart from a sole dependence on the [Formula: see text] quadratic Casimir operator, [Formula: see text], evaluated over the fundamental gauge group representation. Noted in nonrelativistic quark models and in a nonperturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other nonperturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of [Formula: see text]. Though numerically subleading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the nonperturbative fermionic sector of QCD.