  The paper has the form of a proposal concerned with the relationship between
the three mathematically rigorous approaches to quantum field theory: 1) local
algebraic formulation of Haag, 2) Wightman formulation and 3) the perturbative
formulation based on the microlocal renormalization method. In this project we
investigate the relationship between 1) and 3) and utilize the known
relationships between 1) and 2). The main goal of the proposal lies in
obtaining obstructions for the existence of the adiabatic limit (confinement
problem in the phenomenological standard model approach). We extend the method
of deformation of D\"utsch and Fredenhagen (in the Bordeman-Waldmann sense) and
apply Fedosov construction of the formal index -- an analog of the index for
deformed symplectic manifolds, generalizing the Atiyah-Singer index. We present
some first steps in realization of the proposal.
