  We apply to a lattice version of the 't~Hooft model, QCD in two space-time
dimensions for large number of colours, a method recently proposed to obtain an
effective mesonic action starting from the fundamental, fermionic one. The idea
is to pass from a canonical, operatorial representation, where the low-energy
states have a direct physical interpretation in terms of a Bogoliubov vacuum
and its corresponding quasiparticle excitations, to a functional, path integral
representation, via the formalism of the transfer matrix. In this way we obtain
a lattice effective theory for mesons in a self-consistent setting. We also
verify that well-known results from other different approaches are reproduced
in the continuum limit.

High Energy Physics - Lattice