Deformation quantization of the Heisenberg supergroup

Motivated by noncommutative quantum field theory, we construct a  non-formal deformation
quantization of the Heisenberg supergroup. This  deformed star-product provides a universal
deformation formula, namely  it deforms algebras on which the Heisenberg supergroup is acting.
In  this context, we are led to consider the notions of Hilbert superspace  and C*-superalgebra,
compatible with the deformation.