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

Claudio D'Antoni, Gerardo Morsella
November 25, 2005
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.
open access link Rev.Math.Phys.18:565-594,2006; Erratum-ibid.19:567-569,2007
@article{DAntoni:2005htl, author = "D'Antoni, Claudio and Morsella, Gerardo", title = "{Scaling algebras and superselection sectors: Study of a class of models}", journal = "Rev. Math. Phys.", volume = "18", year = "2006", pages = "565-594", doi = "10.1142/S0129055X06002723, 10.1142/S0129055X07003048", note = "[Erratum: Rev. Math. Phys.19,567(2007)]", eprint = "math-ph/0511072", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = MATH-PH/0511072;%%" }

Keywords: 
scaling limits, Superselection Theory