  We calculate the Green functions for a scalar field theory with quartic
interactions for which the fields are multiplied with a generic translation
invariant star product. Our analysis involves both noncommutative products, for
which there is the canonical commutation relation among coordinates, and
nonlocal commutative products. We give explicit expressions for the one-loop
corrections to the two and four point functions. We find that the phenomenon of
ultraviolet/infrared mixing is always a consequence of the presence of
noncommuting variables. The commutative part of the product does not have the
mixing.
