  We show that the Yang-Mills quantum field theory with momentum and spacetime
cutoffs in four Euclidean dimensions is equivalent, term by term in an
appropriately resummed perturbation theory, to a Fermionic theory with nonlocal
interaction terms. When a further momentum cutoff is imposed, this Fermionic
theory has a convergent perturbation expansion. To zeroth order in this
perturbation expansion, the correlation function $E(x,y)$ of generic components
of pairs of connections is given by an explicit, finite-dimensional integral
formula, which we conjecture will behave as $$E(x,y) \sim |x - y|^{-2 - 2
d_G},$$ \noindent for $|x-y|>>0,$ where $d_G$ is a positive integer depending
on the gauge group $G.$ In the case where $G=SU(n),$ we conjecture that $$d_G =
{\rm dim}SU(n) - {\rm dim}S(U(n-1) \times U(1)),$$ \noindent so that the rate
of decay of correlations increases as $n \to \infty.$
