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

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.

28 pages, typos corrected, minor explanations and changes added

References in corpus (1)

• Superselection Sectors and General Covariance.I

Cited by in corpus (5)

• Scaling limits of integrable quantum field theories
• Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
• On dilation symmetries arising from scaling limits
• Representations of nets of C*-algebras over S^1
• Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models