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We present a method of short-distance analysis in quantum field theory thatdoes not require choosing a renormalization prescription a priori. We set outfrom a local net of algebras with associated pointlike quantum fields. The nethas a naturally defined scaling limit in the sense of Buchholz and Verch; weinvestigate the effect of this limit on the pointlike fields. Both for thefields and their operator product expansions, a well-defined limit procedurecan be established. This can always be interpreted in the usual sense ofmultiplicative renormalization, where the renormalization factors aredetermined by our analysis. We also consider the limits of symmetry actions. Inparticular, for suitable limit states, the group of scaling transformationsinduces a dilation symmetry in the limit theory.

Scaling algebras and pointlike fields: A nonperturbative approach to renormalization