't Hooft bound-state equation: A view from two gauges

Two-dimensional $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$-invariant chromodynamics is canonically quantized in both the light-cone and the axial gauges. A principal-value infrared cutoff is adopted. A direct Hamiltonian method leads to two different meson bound-state equations in the limit of $N\to \infty$, $g^{2}N$ kept fixed. In the light-cone gauge, 't Hooft's equation is obtained; in the axial gauge, the corresponding equation suffers from covariance problems rooted in the severe infrared divergences of the theory. The Bose form of the model is also presented.