Symmetries of field theories on the non-commutative plane
  New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a scalar field is coupled to a Chern - Simons gauge field, a geometrical phase emerges for vortex - like solutions, transformed by Galilei boosts. 
P. A. Horvathy, L. Martina, and P.C. Stichel