Scaling Algebras and Superselection Sectors: Study of a Class of Models

TL;DR

This paper investigates a class of quantum field theory models to understand how superselection sectors behave under scaling limits, revealing conditions under which sectors are preserved or lost.

Contribution

It demonstrates a construction of models where superselection sectors correspond to group representations and analyzes their behavior in the scaling limit.

Findings

Sectors associated with G/N are preserved in the scaling limit.

Conditions are derived for the scaling limit of tensor product theories to match the product of their limits.

A framework linking group representations to superselection sectors in quantum field theories.

Abstract

We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R. Verch). In particular, we show that for each pair (G, N), with G a compact Lie group and N a closed normal subgroup, there is a net of observable algebras which has (a subset of) DHR sectors in 1-1 correspondence with classes of irreducible representations of G, and such that only the sectors corresponding to representations of G/N are preserved in the scaling limit. In the way of achieving this result, we derive sufficient conditions under which the scaling limit of a tensor product theory coincides with the product of the scaling limit theories.