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Relative Haag Duality for the Free Field in Fock Representation
, 2008
"... We consider a natural generalization of Haag duality to the case in which the observable algebra is restricted to a subset of the spacetime and is not irreducible: the commutant and the causal complement have to be considered relatively to the ambient space. We prove this relative form of Haag dual ..."
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Cited by 2 (0 self)
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We consider a natural generalization of Haag duality to the case in which the observable algebra is restricted to a subset of the spacetime and is not irreducible: the commutant and the causal complement have to be considered relatively to the ambient space. We prove this relative form of Haag
On Haag Duality for Pure States of Quantum Spin Chain
, 2007
"... Abstract: In this note, we consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semiinfinite intervals (∞, −1] and [0, ∞) when the von Neumann algebra generated by observables localized in [0, ∞) is non type I. ..."
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Abstract: In this note, we consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semiinfinite intervals (∞, −1] and [0, ∞) when the von Neumann algebra generated by observables localized in [0, ∞) is non type I.
Restricted Haag duality in locally covariant quantum field theories
, 2004
"... We investigate a new property of nets of local algebras over 4dimensional globally hyperbolic spacetimes, called restricted Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Restricted Haag duality i ..."
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We investigate a new property of nets of local algebras over 4dimensional globally hyperbolic spacetimes, called restricted Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Restricted Haag duality
Punctured Haag duality in locally covariant quantum field theories
, 2004
"... We investigate a new property of nets of local algebras over 4dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Punctured Haag duality imp ..."
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Cited by 13 (4 self)
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We investigate a new property of nets of local algebras over 4dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Punctured Haag duality
Entanglement, HaagDuality and Type Properties of Infinite Quantum Spin Chains
, 2008
"... We consider an infinite spin chain as a bipartite system consisting of the left and right halfchain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neum ..."
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Cited by 10 (5 self)
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We consider an infinite spin chain as a bipartite system consisting of the left and right halfchain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the halfchains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state ϕS provides a particular example for this type of entanglement.
Modular Structure and Duality in Conformal Quantum Field Theory
 COMMUN.MATH.PHYS
, 1993
"... Making use of a recent result of Borchers, an algebraic version of the BisognanoWichmann theorem is given for conformal quantum field theories, i.e. the TomitaTakesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector concides with the evolution given ..."
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Cited by 77 (29 self)
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by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space M, and Haag duality for double cones holds provided the net of local algebras is extended to a pre
Superselection structure of massive quantum field theories
 in 1 + 1 dimensions, DESYpreprint 97???, hepth/97
"... We show that a large class of massive quantum field theories in 1 + 1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1 dimension ..."
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Cited by 26 (4 self)
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We show that a large class of massive quantum field theories in 1 + 1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1
Results 1  10
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1,122