A note on space noncommutativity

We consider a two-point spatial lattice approximation to an open string mov ing in a fiat background with B field. It gives a constrained dipole system under the influence of a vector potential. Solving and quantizing this sys tem recover all the essential features of a noncommutative space. In partic ular, open string interactions induce a canonical product structure on the Hilbert space of the dipole system. It coincides with the usual star produc t, even though the position operators can be thought of as mutually commuti ng. Modification of gauge transformations in this noncommutative space also naturally emerges. (C) 1999 Published by Elsevier Science B.V. All rights reserved.