  Treating the QCD Wilson loop as amplitude for the propagation of the first
quantized particle we develop the second quantization of the same propagation.
The operator of the particle position $\hat{\cal X}_{\mu}$ (the endpoint of the
"open string") is introduced as a limit of the large $N$ Hermitean matrix. We
then derive the set of equations for the expectation values of the vertex
operators $\VEV{ V(k_1)\dots V(k_n)} $. The remarkable property of these
equations is that they can be expanded at small momenta (less than the QCD mass
scale), and solved for expansion coefficients. This provides the relations for
multiple commutators of position operator, which can be used to construct this
operator. We employ the noncommutative probability theory and find the
expansion of the operator $\hat{\cal X}_\mu $ in terms of products of creation
operators $ a_\mu^{\dagger}$. In general, there are some free parameters left
in this expansion. In two dimensions we fix parameters uniquely from the
symplectic invariance. The Fock space of our theory is much smaller than that
of perturbative QCD, where the creation and annihilation operators were
labelled by continuous momenta. In our case this is a space generated by $d =
4$ creation operators. The corresponding states are given by all sentences made
of the four letter words. We discuss the implication of this construction for
the mass spectra of mesons and glueballs.
