Non-formal deformation quantization of Heisenberg Supergroup's Actions

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 Rieffel’s one: we obtain a Universal Deformation Formula for the actions of Rm|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.