Abstract
In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that space-time coordinates of the open string end-points become non-commutative, and correspondingly the D-brane world-volume also becomes non-commutative. This provides a string theory derivation and generalization of the non-commutativity obtained previously in the M(atrix) model compactification. For Dp-branes with p ≥ 2 our results are new and agree with that of M(atrix) theory for the case of A = 0 (where A is the world-volume gauge field) if the T-duality radii are used. © 1999 Elsevier Science B.V. All rights reserved.