  We construct a non-formal deformation machinery for the actions of the
Heisenberg supergroup analogue to the one developed by M. Rieffel for the
actions of R^d. However, the method used here differs from Rieffel's one: we
obtain a Universal Deformation Formula for the actions of R^{m|n} as a
byproduct of Weyl ordered Kirillov's orbit method adapted to the graded
setting. To do so, we have to introduce the notion of C*-superalgebra, which is
compatible with the deformation, and which can be seen as corresponding to
noncommutative superspaces. We also use this construction to interpret the
renormalizability of a noncommutative Quantum Field Theory.
