Understand
The two-dimensional QCD in the large $N$ limit, generally referred to as the 't Hooft model, is numerically investigated in the axial gauge in a comprehensive manner.
- The corresponding Bethe-Salpeter equation for a bound $q\bar{q}$ pair, originally derived by Bars and Green in 1978, was first numerically tackled by Li and collaborators in late 1980s, yet only for the {\it stationary} mesons.
- In this paper, we make further progress by numerically solving the Bars-Green equation for {\it moving} mesons, ranging from the chiral pion to charmonium.
- By choosing several different quark masses, we computed the corresponding quark condensates, meson spectra and their decay constants for a variety of meson momenta, and found satisfactory agreement with their counterparts obtained using light-cone gauge, thus numerically verified the gauge and Poincar\'{e} invariance of the 't Hooft model.