Deformation quantization for Heisenberg supergroup

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 Rd. However, the method used here differs from Rieffelʼs one: we obtain a Universal Deformation Formula for the actions of Rm|n as a byproduct of Weyl ordered Kirillovʼs 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.