Superselection sectors, whose analysis is one of the major achievements of local quantum physics, have been approached in several ways, depending on the spacetime and the criterion of interest. In the present talk we give a general scheme to define sectors, independent of the above choices. The input is given by a family of spacetime regions, where the sectors are
supposed to be localized, and a factorial Haag-Kastler net fulfilling relative Haag duality on such regions. The output is a superselection structure localized on regions of the given family, covariant with respect to spacetime symmetries preserving the regions themselves.
Our scheme is based on the notion of covariant cohomology of a Haag-Kastler net, and covers all the types of regions previously considered both in (4d) Minkowski space and in curved spacetimes. Moreover, it allows detection of topological phenomena as the Aharonov-Bohm effect. Hypercones (used by Buchholz and Roberts in the massless case) fit our scheme, yet the energetic aspects are the subject of a work in progress with D. Buchholz.
Joint work with F. Ciolli and G. Ruzzi http://arxiv.org/abs/2306.08449
