Hamiltonian approach to QCD_2 in the axial gauge

TL;DR

This paper develops a Hamiltonian framework for two-dimensional QCD in the large N_C limit, explicitly bosonizes the theory, and analyzes meson interactions and chiral properties, including decay mechanisms.

Contribution

It introduces a bosonization and diagonalization method for QCD_2 in the large N_C limit, providing a new way to study meson dynamics and chiral effects.

Findings

Mesons are described as free particles with canonical creation and annihilation operators.

Interactions between mesons are derived from N_C corrections to the Hamiltonian.

The backward motion of the chiral pion significantly contributes to decay amplitudes.

Abstract

The Hamiltonian approach is developed for QCD_2 in the limit of infinite number of colours N_C ('t Hooft model). Bosonization of the theory is performed explicitly and the generalized Bogoliubov transformation for the composite boson operators is introduced and used to bring the Hamiltonian into diagonal form in the two-body sector. The resulting theory is re-formulated in terms of effective degrees of freedom and describes the free mesons with creation and annihilation operators commuting in the canonical way. Corrections in N_C to the leading term in the Hamiltonian describe the interaction between mesons and can be used to consider their decays. Chiral properties of the theory are discussed and it is shown that the backward motion of the chiral pion (Goldstone mode) is not suppressed and should contribute to the decays amplitudes.