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Scaling Algebras and Pointlike Fields: A nonpertubative approach to renormalization

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JournalCommunications in Mathematical Physics
DatePublished - Jan 2009
Issue number2
Volume285
Number of pages36
Pages (from-to)763-798
Original languageEnglish

Abstract

We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.

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