Convergence Theorem for Non-commutative Feynman Graphs and   Renormalization
  We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R^d (NQFT). We give a detailed classification of divergent graphs in some massive NQFT and demonstrate the renormalizability of some of these theories. 
Iouri Chepelev and Radu Roiban