Deformation quantization for Heisenberg supergroup (Q442192)

This paper constructs a non-formal procedure for the deformation quantization of the Heisenberg supergroup. Let us recall that deformation quantization was initiated by Bayen, Flato, Fronsdal, Lichnerowicz and Sternheimer, in order to introduce a non commutative product on the algebra of smooth functions on a Poisson manifold \(M\). In this work, the authors first recall the basic notions of supergeometry. Then they develop a version of Kirillov's orbit method for Heisenberg supergroups. They also introduce a notion of \(C*\)-superalgebra. They apply the results of the paper to noncommutative renormalizable theories and obtain a universal deformation formula which differs from Rieffel's one and which is well-adapted to supergeometry. An interpretation of the harmonic term responsible of the renormalization of the quantum field theory is finally given.