Scaling algebras and pointlike fields: A nonperturbative approach to renormalization

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.

minor changes and clarifications; as to appear in Commun. Math. Phys.; 37 pages

References in corpus (10)

• Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory
• Phase space properties and the short distance structure in quantum field theory
• The operator product expansion for perturbative quantum field theory in curved spacetime
• Operator product expansions as a consequence of phase space properties
• Quarks, gluons, colour: Facts or fiction?
• Quantum Field Theory: Where We Are
• Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples
• Scaling algebras for charged fields and short-distance analysis for localizable and topological charges
• Scaling Algebras and Superselection Sectors: Study of a Class of Models
• A sharpened nuclearity condition and the uniqueness of the vacuum in QFT

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• Charges in the UV completion of neutral electrodynamics
• Spin and Statistics and First Principles
• Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models