Infrared cutoffs and the adiabatic limit in noncommutative spacetime
  We discuss appropriate infrared cutoffs and their adiabatic limit for field theories on the noncommutative Minkowski space in the Yang-Feldman formalism. In order to do this, we consider a mass term as interaction term. We show that an infrared cutoff can be defined quite analogously to the commutative case and that the adiabatic limit of the two-point function exists and coincides with the expectation, to all orders. 
Claus Doescher, Jochen Zahn