Complete integration ofU(N)lattice gauge theory in a large-Nlimit

We present an approximation for the integration over a link in the Feynman path integral for $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ lattice quantum chromodynamics (QCD). The approximation is valid when $N\to \infty$ and $g^{2}N$ is fixed to a large value. The result is such that subsequent link integrations have the same form, allowing a complete evaluation of the path integral in any dimension over the entire lattice by repeated application of the approximation. Our technique can be applied to a variety of problems. As sources for the Yang-Mills field we use quarks traveling on world lines. We present a complete action formulation of Dirac particles on world lines with spin, color, flavor, and mass interacting with the gluon field. Evaluating the meson propagator in such a theory in our approximation we arrive at a previously proposed string model with quarks at the ends, thus demonstrating the dynamical equivalence of strings and QCD in our limit, on the lattice.