Wave operators and  $\hbar$-expansion of Wightman distributions

Quantum field theory (QFT) provides our basic understanding
of physical interactions between elementary particles.  Despite great experimental successes, physical QFT models are ill-defined from the mathematical viewpoint: divergences and infinities appear in the
computation of physical quantities. There are many approaches to address
these problems. A traditional one is the Wightman formalism for
the so-called n-point functions, or Wightman distributions.

In this talk, after briefly reviewing some relevant notions on QFT,
I will present an approach for defining n-point functions which is based on deformation quantization twisted by wave operators of a nonlinear wave equation. Preliminary results on the 2-point function of a simple model show that some of the infinities usually appearing in QFT are absorbed by the twisted deformation.