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In this paper, we study generic non-local NJL models for four-dimensional QCDin the limit of a large number of colours. We diagonalise, through aBogoliubov-type transformation, the Hamiltonian of the model completely interms of the compound operators creating/annihilating mesons - bound states ofdressed quarks and antiquarks - and demonstrate a one-to-one correspondencebetween the Bogoliubov diagonalisation condition and the Bethe-Salpeterequation for bound states. We conclude that, in the leading order in N_C, thenontrivial contents of the theory is entirely encoded in the chiral angle - thesolution to the mass-gap equation for dressed quarks. As a consequence, weextend the statement of existence of excited solutions to the mass-gapequation, called vacuum replicas, beyond the BCS level and prescribe a newindex to the mesonic operators - the label of the vacuum state in which thecorresponding meson is created.Comment: RevTeX4, 37 pages, 5 Postscript figures, uses epsfig.sty, to appear  in Phys.Rev.

Mesonic states and vacuum replicas in potential quark models for QCD