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 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.

Brunetti, R., Ruzzi, G. (2007). Superselection sectors and general covariance. I. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 270(1), 69-108 [10.1007/s00220-006-0147-5].

Superselection sectors and general covariance. I

RUZZI, GIUSEPPE
2007-01-01

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 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.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
Settore MAT/07 - FISICA MATEMATICA
English
QUANTUM-FIELD THEORIES; MULTIPLY CONNECTED SPACE; PARTICLE STATISTICS; LOCAL OBSERVABLES; CURVED SPACETIMES; WICK POLYNOMIALS; COMPACT-GROUPS; TIME; ALGEBRAS; DUALITY
Brunetti, R., Ruzzi, G. (2007). Superselection sectors and general covariance. I. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 270(1), 69-108 [10.1007/s00220-006-0147-5].
Brunetti, R; Ruzzi, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/27710
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