Corrections to the abelian Born-Infeld action arising from noncommutative geometry

In a recent paper Seiberg and Witten have argued that the full actiondescribing the dynamics of coincident branes in the weak coupling regime isinvariant under a specific field redefinition, which replaces the group ofordinary gauge transformations with the one of noncommutative gauge theory.This paper represents a first step towards the classification of invariantactions, in the simpler setting of the abelian single brane theory. Inparticular we consider a simplified model, in which the group of noncommutativegauge transformations is replaced with the group of symplectic diffeomorphismsof the brane world volume. We carefully define what we mean, in this context,by invariant actions, and rederive the known invariance of the Born-Infeldvolume form. With the aid of a simple algebraic tool, which is a generalizationof the Poisson bracket on the brane world volume, we are then able to describeinvariant actions with an arbitrary number of derivatives.Comment: 16 page