THE SCALAR POTENTIAL IN NONCOMMUTATIVE GEOMETRY

We present a derivation of the general form of the scalar potential in Yang-Mills theory of a non-commutative space which is a product of a four-dimensional manifold times a discrete set of points. We show that a non-trivial potential without flat directions is obtained after eli minating the auxiliary fields only if constraints are imposed on the m ass matrices utilised in the Dirac operator. The constraints and poten tial are related to a prepotential function.