Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory

TL;DR

This paper develops a framework for analyzing the short-distance behavior of local quantum field theories using scaling algebras, revealing how theories behave under renormalization and classifying their scaling limits.

Contribution

It introduces a systematic method to construct scaling algebras for local observables in quantum field theory, applicable to various spacetimes, and classifies their scaling limits.

Findings

Every theory has a (possibly non-unique) scaling limit.

Dilation invariant theories are stable under renormalization group actions.

The framework discusses wedge duality and its physical implications.

Abstract

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined.