Nonlocal Condensates in QCD

In the presence of the nontrivial QCD ground state or vacuum, nonlocal condensates are used to characterize the quark or gluon propagator, or other Green functions of higher order. In this paper, we wish to show that, by taking the large $N_c$ limit (with $N_c$ the number of color) in treating higher-order condensates, a closed set of coupled differential equations may be derived for nonlocal condensates. As a specific example, the leading-order equations for the nonlocal condensates appearing in the quark propagator are derived and explicit solutions are obtained. Some applications of our analytical results are briefly discussed.