1,720,975 research outputs found
An algebraic condition for the Bisognano-Wichmann property
Full text linkThe Bisognano-Wichmann property for local, Poincaré 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 masselss 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
The Bisognano–Wichmann Property on Nets of Standard Subspaces, Some Sufficient Conditions
Full text linkWe discuss the Bisognano–Wichmann property for localPoincaré covariant nets of standard subspaces. We provide a sufficient algebraic condition on the covariant representation ensuring the Bisognano–Wichmann and the duality properties without further assumptions on the net. We call it 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 on the relation between the Bisognano–Wichmann property and the split property in the standard subspace setting
Scale and Möbius covariance in two-dimensional Haag–Kastler net
Full text linkGiven a two-dimensional Haag-Kastler net which is Poincare-dilation covariant with additional properties, we prove that it can be extended to a Mobius 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 Poincare-dilation covariant net which cannot be extended to a Mobius covariant net, and discuss the obstructions
The Bisognano–Wichmann property for asymptotically complete massless QFT
Full text linkWe 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
Spacelike deformations: higher-helicity fields from scalar fields
Full text linkIn 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
A family of non-modular covariant AQFTs
Full text linkBased on the construction provided in our paper “Covariant homogeneous nets of standard subspaces”, Comm Math Phys 386:305–358, (2021), we construct non-modular covariant one-particle nets on the two-dimensional de Sitter spacetime and on the three-dimensional Minkowski space
Covariant homogeneous nets of standard subspaces
Full text linkRindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti–Guido–Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a Z2-graded Lie group we define a (twisted-)local poset of abstract wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges and study special wedge configurations. This allows us to exhibit an analog of the Haag–Kastler one-particle net axioms for such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL construction. The construction is possible for a large family of Lie groups and provides several new models. We further comment on orthogonal wedges and extension of symmetries
Conformal Covariance and the Split Property
Full text linkWe 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, Möbius 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 2-dimensional Minkowski space, which—although being diffeomorphism covariant—does not have the split property. © 2017 The Author(s
From Euler elements and 3-gradings to non-compactly causal symmetric spaces
No full textWe discuss the interplay between causal structures of symmetric spaces and geometric aspects of Algebraic Quantum Field Theory (AQFT). The central focus is the set of Euler elements in a Lie algebra, i.e., elements whose adjoint action defines a 3-grading. In the first half of this article we survey the classification of reductive causal symmetric spaces from the perspective of Euler elements. This point of view is motivated by recent applications in AQFT. In the second half we obtain several results that prepare the exploration of the deeper connection between the structure of causal symmetric spaces and AQFT. In particular, we explore the technique of strongly orthogonal roots and corresponding systems of sl2-subalgebras. Furthermore, we exhibit real Matsuki crowns in the adjoint orbits of Euler elements and we describe the group of connected components of the stabilizer group of Euler elements
Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality
No full textThe current article continues our project on representation theory, Euler elements, causal homogeneous spaces and Algebraic Quantum Field Theory (AQFT). We call a pair (h,k) of Euler elements orthogonal if eπiadhk=-k. We show that, if (h,k) and (k,h) are orthogonal, then they generate a 3-dimensional simple subalgebra. We also classify orthogonal Euler pairs in simple Lie algebras and determine the fundamental groups of orbits of Euler elements in arbitrary finite-dimensional Lie algebras. Causal complements of wedge regions in spacetimes can be related to so-called twisted complements in the space of abstract Euler wedges, defined in purely group theoretic terms. We show that any pair of twisted complements can be connected by a chain of successive complements coming from 3-dimensional subalgebras
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