Scaling algebras and pointlike fields: A nonperturbative approach to renormalization

TL;DR

This paper introduces a nonperturbative method for analyzing short-distance behavior in quantum field theory using scaling limits of local nets of algebras, clarifying renormalization and symmetry transformations.

Contribution

It develops a framework for studying the scaling limit of quantum fields without predefined renormalization schemes, linking it to operator product expansions and symmetry actions.

Findings

Well-defined scaling limits for pointlike fields and their operator product expansions.

Renormalization factors can be derived from the scaling limit analysis.

Scaling transformations induce dilation symmetry in the limit theory.

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.