  In the Wilson's lattice formulation of QCD, a fermionic Fock space of states
can be explicitly built at each time slice using canonical creation and
annihilation operators. The partition function $Z$ is then represented as the
trace of the transfer matrix, and its usual functional representation as a path
integral of $\exp(- S)$ can be recovered in a standard way. However, applying a
Bogoliubov transformation on the canonical operators before passing to the
functional formalism, we can isolate a vacuum contribution in the resulting
action which depends only on the parameters of the transformation and fixes
them via a variational principle. Then, inserting in the trace defining $Z$ an
operator projecting on the mesons subspace at each time slice and making the
physical assumption that the true partition function is well approximate by the
projected one, we can also write an effective quadratic action for mesons. We
tested the method in the renowned 't Hooft model, namely QCD in two spacetime
dimensions for large number of colours, in Coulomb gauge.
