Non commutative geometry and super Yang-Mills theory

We aim to connect the non commutative geometry "quotient space" viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory, This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size Sigma/N with the boundary condition given by a system with p units of magnetic flux. The transition to irrational parameter san be obtained by letting Ai and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification. (C) 1999 published by Elsevier Science B,V, All rights reserved.