Scaling limit for subsystems and Doplicher-Roberts reconstruction

TL;DR

This paper investigates the structure of scaling limits in local nets within quantum field theory, establishing conditions for the uniqueness of scaling limits and explicitly computing limits for free field theories.

Contribution

It provides new conditions under which the scaling limit of a subsystem matches that of the larger system, and explicitly computes the scaling limit of fixpoint nets in free field theories.

Findings

Conditions for the uniqueness of scaling limits in free field theories.

Explicit computation of the scaling limit of fixpoint nets.

Sufficient conditions for the equality of canonical field nets in scaling limits.

Abstract

Given an inclusion $B \subset F$ of (graded) local nets, we analyse the structure of the corresponding inclusion of scaling limit nets $B_0 \subset F_0$, giving conditions, fulfilled in free field theory, under which the unicity of the scaling limit of $F$ implies that of the scaling limit of $B$. As a byproduct, we compute explicitly the (unique) scaling limit of the fixpoint nets of scalar free field theories. In the particular case of an inclusion $A \subset B$ of local nets with the same canonical field net $F$, we find sufficient conditions which entail the equality of the canonical field nets of $A_0$ and $B_0$.