Limit transition to the light-front QCD and a quark–antiquark approximation

We consider a transition to the light-front quantum chromodynamics from theories quantized on spacelike planes that approach the light front. This limit transition differs for zero and nonzero modes, which leads to the appearance of a semiphenomenological parameter that can be used to describe confinement effects. As an illustration, we consider the problem of the bound states of a quark–antiquark pair in $2{+}1$ dimensions. We use a lattice gauge-invariant regularization in the transverse space and consequently obtain an analogue of the 't Hooft equation. We also discuss the possibility of calculating the spectrum of bound states in $3{+}1$ dimensions.