  The quantization of the non-commutative N=1, U(1) super-Yang-Mills action is
performed in the superfield formalism. We calculate the one-loop corrections to
the self-energy of the vector superfield. Although the power-counting theorem
predicts quadratic ultraviolet and infrared divergences, there are actually
only logarithmic UV and IR divergences, which is a crucial feature of
non-commutative supersymmetric field theories.
