München 1997 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP XII: HV XII

MP XII.1: Invited Talk

Friday, March 21, 1997, 09:45–10:30, HS 118

Superselection Structure of massive Quantum Field Theories in 1+1 Dimensions — •M. Müger — II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D–22761 Hamburg

We show that a large class of massive quantum field theories in 1+1 dimensions 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 charges which are localizable in wedge regions are ruled out. Furthermore, Haag duality holds in all locally normal irreducible representations provided this is the case in the vacuum representation. This leads to new results pertaining to soliton sectors. Some remarks are made concerning the representation theory of observables in situations where the vacuum sector satisfies only the weaker property of wedge duality. The no-go theorem as well as the other results rely on the split property for wedge regions. It must be emphasized that massless theories do not have this property. (In particular, positive energy representations of conformally invariant theories are known to be DHR representations.)