Seiberg-Witten map and Galilean symmetry violation in a non-commutative planar system

Abstract

An effective U(1) gauge invariant theory is constructed for a non-commutative Schrodinger field coupled to a background U(1)_{\star} gauge field in 2+1-dimensions using first order Seiberg-Witten map. We show that this effective theory can be cast in the form of usual Schrodinger action with interaction terms of noncommutative origin provided the gauge field is of ``background'' type with constant magnetic field. The Galilean symmetry is investigated and a violation is found in the boost sector. We also consider the problem of Hall conductivity in this framework.

REVTeX, 4 pages, Title changed, Paper shortened, Appendix removed, A new section on Galilean symmetry added