As an application of Roberts ’ net cohomology theory, we positively answer about the completeness of the known set of DHR sectors of the observables of the model in the title, detailed in [7]. This result is achieved via the triviality of the 1-cohomology of the underlying causal index poset with values in the field net, enhancing this tool for the case of Weyl nets not satisfying the split property and with anyonic commutation rules. We also take advantage of different causal index posets for the nets involved, and obtain the description of the twisted and untwisted sectors of the

We continue studying net bundles over partially ordered sets (posets), defined as the analogues of ordinary fibre bundles. To this end, we analyze the connection between homotopy, net homology and net cohomology of a poset, giving versions of classical Hurewicz theorems. Focusing our attention on Hilbert net bundles, we define the K-theory of a poset and introduce functions over the homotopy groupoid satisfying the same formal properties as Chern classes. As when the given poset is a subbase for the topology of a space, our results apply to the category of locally constant bundles.

emergence of new superselection sectors

In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We develop a theory of connections and curvature for bundles over posets in search of a formulation of gauge theories in algebraic quantum field theory. 2