Dynamics of Wilson observables in non-commutative gauge theory

An equation for the quantum average of the gauge invariant Wilson loop in n on-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang- Mills theory. At finite N, the equation involves the quantum averages of th e additional gauge invariant observables of the non-commutative theory asso ciated with open contours in space-time. We also derive equations for corre lators of several gauge invariant (open or closed) Wilson lines. Finally, w e discuss a perturbative check of our results. (C) 2001 Elsevier Science B. V. All rights reserved.