  In this paper, we study generic non-local NJL models for four-dimensional QCD
in the limit of a large number of colours. We diagonalise, through a
Bogoliubov-type transformation, the Hamiltonian of the model completely in
terms of the compound operators creating/annihilating mesons - bound states of
dressed quarks and antiquarks - and demonstrate a one-to-one correspondence
between the Bogoliubov diagonalisation condition and the Bethe-Salpeter
equation for bound states. We conclude that, in the leading order in N_C, the
nontrivial contents of the theory is entirely encoded in the chiral angle - the
solution to the mass-gap equation for dressed quarks. As a consequence, we
extend the statement of existence of excited solutions to the mass-gap
equation, called vacuum replicas, beyond the BCS level and prescribe a new
index to the mesonic operators - the label of the vacuum state in which the
corresponding meson is created.
