/ 05 06 08 4 v 1 1 0 Ju n 20 05 The AdS particle

In this note we have considered a relativistic Nambu-Goto model for a particle in AdS metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed [7] " Exotic Oscillator ". The Snyder algebra and subsequently the κ-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncom-mutative spacetime in the context of open string where only a curved target space is introduced. 1 Introduction: It is now accepted in the High Energy Physics community that nonlocality in quantum field theory, or in a more fundamental way the fuzziness (or Non-Commutativity (NC)) in space(time), will be an integral part of present-day theories. Intuitive arguments that are used in avoiding the paradoxes one faces in trying to localize a spacetime point within the Planck length [1] lead to a lower-bound in spacetime interval. This feature is also favored in the modifications of the Heisenberg uncertainty principle that one obtains in string scattering results (see for example [1]). It was first demonstrated by Snyder [2] that Lorentz invariance and discretization requires an NC spacetime. The NC spacetime has been revived by the seminal work of Seiberg and Witten [3] who explicitly demonstrated the emergence of NC manifold in certain low energy limit of open strings moving in the background of a two form gauge field. In this instance, the NC spacetime is expressed by the Poisson bracket algebra (to be interpreted as commutators in the quantum analogue), {x µ , x ν } = θ µν , (1)