20th LQP Workshop

Foundations and constructive aspects of QFT

June 29-30, 2007


Leipzig University

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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Info: Rainer Verch
ITP, Universitaet Leipzig
Vor dem Hospitaltore 1
Phone: +49 341 97 32423