Translation-invariant models for non-commutative gauge fields
  Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field (see arXiv:0802.0791 [math-ph]), we introduce models for non-commutative U(1) gauge fields along the same lines. More precisely, we include some extra terms into the action with the aim of getting rid of the UV/IR mixing. 
Daniel N. Blaschke, Francois Gieres, Erwin Kronberger, Manfred   Schweda, Michael Wohlgenannt