As a generalization of DHR analysis, the superselection sectors are studied in the absence of the spectrum condition for the reference representation. Considering a net of local observables in 4-dimensional Minkowski spacetime, we associate to a set of representations, that are local excitations of a reference representation fulfilling Haag duality, a symmetric tensor C*-category B(Θ) of bimodules of the net, with subobjects and direct sums. The existence of conjugates is studied introducing an equivalent formulation of the theory in terms of the presheaf associated with the observable net. This allows us to find, under the assumption that the local algebras in the reference representation are properly infinite, necessary and sufficient conditions for the existence of conjugates. Moreover, we present several results that suggest how the mentioned assumption on the reference representation can be considered essential also in the case of theories in curved spacetimes.

Ruzzi, G. (2003). Essential properties of the vacuum sector for a theory of superselection sectors. REVIEWS IN MATHEMATICAL PHYSICS, 15(10), 1255-1283 [10.1142/S0129055X03001874].

Essential properties of the vacuum sector for a theory of superselection sectors

RUZZI, GIUSEPPE
2003

Abstract

As a generalization of DHR analysis, the superselection sectors are studied in the absence of the spectrum condition for the reference representation. Considering a net of local observables in 4-dimensional Minkowski spacetime, we associate to a set of representations, that are local excitations of a reference representation fulfilling Haag duality, a symmetric tensor C*-category B(Θ) of bimodules of the net, with subobjects and direct sums. The existence of conjugates is studied introducing an equivalent formulation of the theory in terms of the presheaf associated with the observable net. This allows us to find, under the assumption that the local algebras in the reference representation are properly infinite, necessary and sufficient conditions for the existence of conjugates. Moreover, we present several results that suggest how the mentioned assumption on the reference representation can be considered essential also in the case of theories in curved spacetimes.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
Settore MAT/07 - Fisica Matematica
English
Con Impact Factor ISI
Generalized vacuum state; Spectrum condition; Superselection sectors
Ruzzi, G. (2003). Essential properties of the vacuum sector for a theory of superselection sectors. REVIEWS IN MATHEMATICAL PHYSICS, 15(10), 1255-1283 [10.1142/S0129055X03001874].
Ruzzi, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/44650
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