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

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

2005-11-25

arxiv.org/abs/math-ph/0511072v2

Rev.Math.Phys.18:565-594,2006; Erratum-ibid.19:567-569,2007

Physics

Mathematical Physics

28 pages, typos corrected, minor explanations and changes added

Scientific paper

10.1142/S0129055X06002723 10.114

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.

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