  In this paper we elaborate on the translation-invariant renormalizable Phi^4
theory in 4-dimensional non-commutative space which was recently introduced by
the Orsay group. By explicitly performing Feynman graph calculations at one
loop and higher orders we illustrate the mechanism which overcomes the UV/IR
mixing problem and ultimately leads to a renormalizable model. The obtained
results show that the IR divergences are also suppressed in the massless case,
which is of importance for the gauge field theoretic generalization of the
scalar field model.
