This talk is an introduction to an unconventional approach to pert. QFT:

• Fields are functionals on the configuration space, which are not restricted by any field equation (``off-shell'' fields).
• Quantization of the free theory is done by deformation of the classical product (i.e., the pointwise product of functionals).
• The interacting quantum theory is treated as a perturbative expansion around the free quantum theory, which is defined by axioms, the most important one being causality.

All solutions of the axioms are constructed. The set of solutions is the orbit of the Stückelberg-Petermann renormalization group when acting on a particular solution.

The interaction is adiabatically switched off. Hence, the IR-problem is separated from the UV-problem. The adiabatic limit (i.e., the limit removing this unphysical switching) is performed only at the end of the construction; typically it exists only for observable quantities. However, local, algebraic properties of the observables can be obtained without performing the adiabatic limit.
Paper