263 research outputs found

    The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions

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    We discuss the Bisognano-Wichmann property for local Poincar\'e covariant nets of standard subspaces. We give a sufficient algebraic condition on the covariant representation ensuring the Bisognano-Wichmann and Duality properties without further assumptions on the net called modularity condition. It holds for direct integrals of scalar massive and massless representations. We present a class of massive modular covariant nets not satisfying the Bisognano-Wichmann property. Furthermore, we give an outlook in the standard subspace setting on the relation between the Bisognano-Wichmann property and the Split property.Comment: Final version. To appear in Annales Henri Poincar\'

    An algebraic condition for the Bisognano-Wichmann Property

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    The Bisognano-Wichmann property for local, Poincar\'e covariant nets of standard subspaces is discussed. We present a sufficient algebraic condition on the covariant representation ensuring Bisognano-Wichmann and Duality properties without further assumptions on the net. Our modularity condition holds for direct integrals of scalar massive and massless representations. We conclude that in these cases the Bisognano-Wichmann property is much weaker than the Split property. Furthermore, we present a class of massive modular covariant nets not satisfying the Bisognano-Wichmann property.Comment: Invited contribution to the Proceedings of the 14th Marcel Grossmann Meeting - MG14 (Rome, 2015

    Spacelike deformations: Higher-helicity fields from scalar fields

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    In contrast to Hamiltonian perturbation theory which changes the time evolution, "spacelike deformations" proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of spacelike deformations of the complex massless Klein-Gordon quantum field into fields of higher helicity. A similar but simpler instance of spacelike deformation allows to increase the mass of scalar fields.Comment: v2: 18p, largely extended and more results added. Title adjuste

    Conformal covariance and the split property

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    We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, M\"obius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which - although being diffeomorphism covariant - does not have the split property.Comment: 34 pages, 3 tikz figure

    Parent and Teacher Perceptions of the Importance and Effectiveness of an Individual Education Program

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    In 1975, Congress passed the Education of All Handicapped Children Act (P.L. 94-142) which had profound effects on the provision of special education services to handicapped children. The law mandated that every student identified as handicapped be provided with an individual education program (IEP). The IEP was to be developed in a meeting attended by a representative of the local educational agency, the child\u27s teacher(s), parents of the child, and, when appropriate, the child. The individualized education program plan is to contain statements of the child\u27s current level of performance, annual goals and short-term objectives, the specific special education services to be provided to the child, the extent to which the child will be able to participate in regular education programs, the expected dates of initiation of services and projected duration of services, and the objective criteria by which progress toward the short-term objective will be measured, as well as a schedule for reviewing (at least on an annual basis) the IEP. In addition, procedural safeguards were described for ensuring that parents of handicapped students had sufficient opportunity to participate in decision making, obtain information relevant to the IEP and appeal decisions they believed were inappropriate

    Split property for free massless finite helicity fields

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    We prove the split property for any finite helicity free quantum fields. Finite helicity Poincar\'e representations extend to the conformal group and the conformal covariance plays an essential role in the argument. The split property is ensured by the trace class condition: Tr (exp(-s L_0)) is finite for all s>0 where L_0 is the conformal Hamiltonian of the M\"obius covariant restriction of the net on the time axis. We extend the argument for the scalar case presented in [7]. We provide the direct sum decomposition into irreducible representations of the conformal extension of any helicity-h representation to the subgroup of transformations fixing the time axis. Our analysis provides new relations among finite helicity representations and suggests a new construction for representations and free quantum fields with non-zero helicity.Comment: v2: Minor corrections, comments and references added, as to appear in Ann. H. Poin

    The Bisognano–Wichmann property for asymptotically complete massless QFT

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    We prove the Bisognano–Wichmann property for asymptotically complete Haag–Kastler theories of massless particles. These particles should either be scalar or appear as a direct sum of two opposite integer helicities, thus, e.g., photons are covered. The argument relies on a modularity condition formulated recently by one of us (VM) and on the Buchholz’ scattering theory of massless particles

    The Bisognano-Wichmann property for asymptotically complete massless QFT

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    We prove the Bisognano-Wichmann property for asymptotically complete Haag-Kastler theories of massless particles. These particles should either be scalar or appear as a direct sum of two opposite integer helicities, thus, e.g., photons are covered. The argument relies on a modularity condition formulated recently by one of us (VM) and on the Buchholz' scattering theory of massless particles.Comment: 30 page

    From local nets to Euler elements

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    Various aspects of the geometric setting of Algebraic Quantum Field Theory (AQFT) models related to representations of the Poincar\'e group can be studied for general Lie groups, whose Lie algebra contains an Euler element, i.e., ad h is diagonalizable with eigenvalues in {-1,0,1}. This has been explored by the authors and their collaborators during recent years. A key property in this construction is the Bisognano-Wichmann property (thermal property for wedge region algebras) concerning the geometric implementation of modular groups of local algebras. In the present paper we prove that under a natural regularity condition, geometrically implemented modular groups arising from the Bisognano-Wichmann property, are always generated by Euler elements. We also show the converse, namely that in presence of Euler elements and the Bisognano-Wichmann property, regularity and localizability hold in a quite general setting. Lastly we show that, in this generalized AQFT, in the vacuum representation, under analogous assumptions (regularity and Bisognano-Wichmann), the von Neumann algebras associated to wedge regions are type III_1 factors, a property that is well-known in the AQFT context.Comment: 65 page

    Scale and M\"obius covariance in two-dimensional Haag-Kastler net

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    Given a two-dimensional Haag-Kastler net which is Poincar\'e-dilation covariant with additional properties, we prove that it can be extended to a M\"obius covariant net. Additional properties are either a certain condition on modular covariance, or a variant of strong additivity. The proof relies neither on the existence of stress-energy tensor nor any assumption on scaling dimensions. We exhibit some examples of Poincar\'e-dilation covariant net which cannot be extended to a M\"obius covariant net, and discuss the obstructions.Comment: 35 pages, 9 Tikz figures. See http://www.mat.uniroma2.it/~tanimoto/smc18.pdf for figures with better fadin
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