't Hooft model in the temporal gauge

TL;DR

This paper analyzes the 't Hooft model in 2D QCD using the temporal gauge, deriving bound state wave functions analytically and exploring their frame dependence and contributions from negative kinetic energy quarks.

Contribution

It provides an analytical derivation of the bound state wave function in the temporal gauge without relying on propagators, highlighting frame dependence and negative energy contributions.

Findings

Wave function expressed as a $_1F_1$ hypergeometric function.

In the infinite momentum frame, the wave function satisfies the 't Hooft equation.

Negative kinetic energy quark contributions persist in all frames.

Abstract

I consider QCD$_2$ in the $N_c \to \infty$ limit at fixed $g^2N_c$. 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 $_1F_1$ 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.