Hamiltonian approach to QCD_2 in the axial gauge

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.