Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-05-05
Rev.Math.Phys. 10 (1998) 1147-1170
Physics
High Energy Physics
High Energy Physics - Theory
latex2e, 21 pages. Final version, to appear in Rev. Math. Phys. Some improvements of the presentation, but no essential change
Scientific paper
10.1142/S0129055X98000380
We show that a large class of massive quantum field theories in 1+1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1 dimensions due to Fredenhagen, Rehren and Schroer is vacuous for such theories. Even charged representations which are localizable only in wedge regions are ruled out. Furthermore, Haag duality holds in all locally normal representations. These results are applied to the theory of soliton sectors. Furthermore, the extension of localized representations of a non-Haag dual net to the dual net is reconsidered. It must be emphasized that these statements do not apply to massless theories since they do not satisfy the above split property. In particular, it is known that positive energy representations of conformally invariant theories are DHR representations.
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