't Hooft model in the temporal gauge

Abstract

I consider QCD${}_2$ in the $N_c\to \infty$ limit at fixed $g^2{N}_c$. The derivation starts from equal-time $q\bar{q}$ bound states in coordinate space and temporal ($A^0=0$) gauge, avoiding the use of quark and gluon propagators. The wave function is given analytically by a ${}_1{F}_1$ function with an explicit frame dependence. In the infinite momentum frame the Fourier transformed wave function satisfies the 't~Hooft equation, however with contributions also from quarks with negative kinetic energy. Such contributions are present also in the rest frame, and do not vanish under boosts.

19 pages, 1 figure