# Henning Bostelmann

# Scaling algebras and pointlike fields

** Abstract: **

The concept of scaling limits plays an important role in high energy physics.
It is based on the expectation that at short distance, a quantum field theory
can be approximated by a simpler theory, its scaling limit. This scaling limit
theory may have very different properties from the original theory, e.g. it
can be a free theory (asymptotic freedom). For a mathematical description of
these limits, a very natural approach has been proposed by Buchholz and Verch
in the framework of algebraic quantum field theory. It is however unclear how
it relates to more usual approaches, in particular to the renormalization of
quantum fields. In order to clear up this matter, we consider models of
algebraic quantum field theory with associated pointlike Wightman fields. We
find that the Buchholz-Verch scaling limit leads to a multiplicative
renormalization scheme for the fields, as expected from perturbation theory.
However, the renormalization factors, which are usually added to the model as
a technical input, turn up as a consequence of our analysis; they can be
computed rather than postulated. In particular, all n-point functions and OPE
coefficients automatically converge in the scaling limit.