Hamiltonian approach to the bound state problem in QCD_2

TL;DR

This paper applies a Hamiltonian and bosonization approach to two-dimensional QCD in the large N_C limit, deriving bound state equations and explicitly finding the chiral pion solution, thus advancing understanding of non-perturbative QCD in lower dimensions.

Contribution

It introduces a Hamiltonian framework with generalized Bogoliubov transformation to analyze bound states and chiral properties in 2D QCD, providing explicit solutions for the massless pion.

Findings

Derived bound state equation in 2D QCD

Explicitly found the chiral pion solution

Discussed chiral symmetry properties

Abstract

Bosonization of the two-dimensional QCD in the large N_C limit is performed in the framework of Hamiltonian approach in the Coulomb gauge. The generalized Bogoliubov transformation is applied to diagonalize the Hamiltonian in the bosonic sector of the theory, and the composite operators creating/annihilating bosons are obtained in terms of dressed quark operators. The bound state equation is reconstructed as a result of the generalized Bogoliubov transformation, and the form of its massless solution, chiral pion, is found explicitly. Chiral properties of the theory are discussed.