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Superselection sectors and general covariance. I
, 2008
"... This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analize sharply localizable charges, and use netcohomology of J.E. Roberts as a main tool. We show that to any 4dimensional globally hyperbolic spaceti ..."
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This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analize sharply localizable charges, and use netcohomology of J.E. Roberts as a main tool. We show that to any 4dimensional globally hyperbolic spacetime it is attached a unique, up to equivalence, symmetric tensor C∗−category with conjugates (in case of finite statistics); 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 shortdistance asymptotic behaviour.
Some Remarks on Group Bundles and C*dynamical systems
, 2008
"... We introduce the notion of fibred action of a group bundle on a C0(X)algebra. By using such a notion, a characterization in terms of induced C*bundles is given for C*dynamical systems such that the relative commutant of the fixedpoint C*algebra is minimal (i.e., it is generated by the centre of ..."
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Cited by 2 (2 self)
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We introduce the notion of fibred action of a group bundle on a C0(X)algebra. By using such a notion, a characterization in terms of induced C*bundles is given for C*dynamical systems such that the relative commutant of the fixedpoint C*algebra is minimal (i.e., it is generated by the centre of the given C*algebra and the centre of the fixedpoint C*algebra). A class of examples in the setting of the Cuntz algebra is given, and connections with superselection structures with nontrivial centre are discussed.
Topological features of massive bosons on two dimensional Einstein spacetime. I: Spatial approach.
, 2009
"... In this paper we tackle the problem of constructing explicit examples of topological cocycles of Robert’s net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some cru ..."
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In this paper we tackle the problem of constructing explicit examples of topological cocycles of Robert’s net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the construction of the topological cocycles. All constructed cocycles lead to unitarily equivalent representations of the fundamental group of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces). The construction is carried out using only Cauchy data and related net of local algebras on the circle. A spacetime approach is considered in a forthcoming paper.