On dilation symmetries arising from scaling limits

TL;DR

This paper explores the emergence of dilation symmetries in quantum field theories at short scales through scaling limits, analyzing their structure in a nonperturbative, model-independent manner.

Contribution

It provides a nonperturbative analysis of dilation symmetries in scaling limit theories, considering non-pure vacuum states and their decompositions.

Findings

Dilation symmetry can be understood via state decompositions.

Conditions on states restrict the form of dilation symmetry.

Analysis is model-independent and nonperturbative.

Abstract

Quantum field theories, at short scales, can be approximated by a scaling limit theory. In this approximation, an additional symmetry is gained, namely dilation covariance. To understand the structure of this dilation symmetry, we investigate it in a nonperturbative, model independent context. To that end, it turns out to be necessary to consider non-pure vacuum states in the limit. These can be decomposed into an integral of pure states; we investigate how the symmetries and observables of the theory behave under this decomposition. In particular, we consider several natural conditions of increasing strength that yield restrictions on the decomposed dilation symmetry.