Interactions and non-commutativity in quantum Hall systems

Abstract

We discuss the role that interactions play in the non-commutative structure\nthat arises when the relative coordinates of two interacting particles are\nprojected onto the lowest Landau level. It is shown that the interactions in\ngeneral renormalize the non-commutative parameter away from the non-interacting\nvalue $\\frac{1}{B}$. The effective non-commutative parameter is in general also\nangular momentum dependent. An heuristic argument, based on the non-commutative\ncoordinates, is given to find the filling fractions at incompressibilty, which\nare in general renormalized by the interactions, and the results are consistent\nwith known results in the case of singular magnetic fields.\n Comment: 8 pages, 2 figures