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Superselection Sectors and General Covariance. I

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Abstract

This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analyze sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool. We show that to any 4-dimensional globally hyperbolic spacetime a unique, up to equivalence, symmetric tensor \({\mathrm{C}^*}\) -category with conjugates (in case of finite statistics) is attached; to any embedding between different spacetimes, the corresponding categories can be embedded, contravariantly, in such a way that all the charged quantum numbers of sectors are preserved. This entails that to any spacetime is associated a unique gauge group, up to isomorphisms, and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups. This form of covariance between sectors also brings to light the issue whether local and global sectors are the same. We conjecture this holds that at least on simply connected spacetimes. It is argued that the possible failure might be related to the presence of topological charges. Our analysis seems to describe theories which have a well defined short-distance asymptotic behaviour.

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Authors and Affiliations

  1. II Institute für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761, Hamburg, Germany

    Romeo Brunetti

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133, Roma, Italy

    Giuseppe Ruzzi

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  1. Romeo Brunetti
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  2. Giuseppe Ruzzi
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Correspondence to Giuseppe Ruzzi.

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Communicated by Y. Kawahigashi

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Brunetti, R., Ruzzi, G. Superselection Sectors and General Covariance. I. Commun. Math. Phys. 270, 69–108 (2007). https://doi.org/10.1007/s00220-006-0147-5

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  • DOI: https://doi.org/10.1007/s00220-006-0147-5

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