263 research outputs found
The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions
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
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
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
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
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
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
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
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
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
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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