A new formalism for the perturbative construction of algebraic
quantum field theory is developed. The formalism allows the treatment
of low-dimensional theories and of non-polynomial interactions. We discuss
the connection between the Stückelberg–Petermann renormalization
group which describes the freedom in the perturbative construction with the
Wilsonian idea of theories at different scales. In particular, we relate
the approach to renormalization in terms of Polchinski’s Flow Equation to
the Epstein–Glaser method. We also show that the renormalization group
in the sense of Gell–Mann–Low (which characterizes the behaviour of the
theory under the change of all scales) is a one-parametric subfamily of the
Stückelberg–Petermann group and that this subfamily is in general only
a cocycle. Since the algebraic structure of the Stückelberg–Petermann
group does not depend on global quantities, this group can be formulated
in the (algebraic) adiabatic limit without meeting any infrared divergencies.
In particular we derive an algebraic version of the Callan–Symanzik
equation and define the β-function in a state independent way.