### Henning Bostelmann
(U Roma II)

## A non-perturbative approach to field renormalization

Renormalization has been a well-known concept in quantum field theory
since decades; it governs our understanding of the short-distance
structure of QCD (quarks, gluons, etc.), and the related notion of
asymptotic freedom is highly appraised. Yet in a non-perturbative,
mathematically precise setting, little is known about these structures.
More recently, Buchholz and Verch introduced a non-perturbative concept
of short distance analysis, which allows to define the scaling limit of
any Haag-Kastler quantum field theory. This approach is very general,
since it abstracts from the renormalization of quantum fields and their
field strenghts; in fact, it does not require that the theory in
question is related to any pointlike fields at all.
But suppose that we have an algebraic theory which does contain
pointlike (Wightman) fields. How is the Buchholz-Verch scaling limit related
to the usual notion of renormalization? This talk aims at clarifying this
relationship, and shows how to recover the action of the scaling
transformations on the fields ("renormalization factors"), which are hidden in
the algebraic approach.

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