Abstract Twisted Duality for Quantum Free Fermi Fields

Foit, Jerzy J.

doi:10.2977/prims/1195182448

Cited by 20 publications

(26 citation statements)

References 7 publications

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“…This assignment (22) respects the lattice structure, as originally proven in [1] (Bose case) and [10] (Fermi case). The modular operators were computed in [9,21,10]. For convenience, we state these properties in the following proposition with a sketch of proof.…”

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confidence: 64%

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Where Infinite Spin Particles are Localizable

Longo

Morinelli

Rehren

2015

Commun. Math. Phys.

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Particle states transforming in one of the infinite spin representations of the Poincaré group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state cannot exist. While it is known that infinite spin states localized in a spacelike cone are dense in the one-particle space, we show here that the subspace of states localized in any double cone is trivial. This implies that the free field theory associated with infinite spin has no observables localized in bounded regions. In an interacting theory, if the vacuum vector is cyclic for a double cone local algebra, then the theory does not contain infinite spin representations. We also prove that if a Doplicher-Haag-Roberts representation (localized in a double cone) of a local net is covariant under a unitary representation of the Poincaré group containing infinite spin, then it has infinite statistics. These results hold under the natural assumption of the Bisognano-Wichmann property, and we give a counter-example (with continuous particle degeneracy) without this property where the conclusions fail. Our results hold true in any spacetime dimension s + 1 where infinite spin representations exist, namely s ≥ 2.

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confidence: 64%

“…with Ω the Fock vacuum vector (see [10]). By the uniqueness of the polar decomposition, we then have J + H = Γ + (J H ), J − H = ZΓ − (iJ H ) and ∆ ± H = Γ ± (∆ H ).…”

mentioning

confidence: 99%

Where Infinite Spin Particles are Localizable

Longo

Morinelli

Rehren

2015

Commun. Math. Phys.

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“…Let H be a standard subspace and R(H) be its second quantization. Second quantization of modular operators were computed in [13,21,17]. Consider the following proposition: Proposition 6.3.…”

Section: Discussionmentioning

confidence: 99%

The Bisognano–Wichmann Property on Nets of Standard Subspaces, Some Sufficient Conditions

Morinelli

2017

Ann. Henri Poincaré

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We discuss the Bisognano-Wichmann property for local Poincaré 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.

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“…densely defined on the Fermonic Fock space F ω . The 1-particle operators are conveniently described in terms of "standard subspaces" [23,25]. Define…”

Section: Tomita-takesaki Theorymentioning

confidence: 99%

Relative entanglement entropy for widely separated regions in curved spacetime

Hollands

Islam

Sanders

2018

Journal of Mathematical Physics

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We give an upper bound of the relative entanglement entropy of the ground state of a massive Dirac-Majorana field across two widely separated regions A and B in a static slice of an ultrastatic Lorentzian spacetime. Our bound decays exponentially in dist(A, B), at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation our result is that, on a manifold with positive spatial scalar curvature, one cannot use the entanglement of the vacuum state to teleport one classical bit from A to B if their distance is of the order of the maximum of the curvature radius and the Compton wave length or greater.

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Abstract Twisted Duality for Quantum Free Fermi Fields

Abstract: Using the properties of standard subspaces of the 1-particle space for the free Fermi field we prove the twisted duality for the von Neumann algebras associated with real closed subspaces. This is done by application of the Tomita-Takesaki theory.

Cited by 20 publications

References 7 publications

Where Infinite Spin Particles are Localizable

Where Infinite Spin Particles are Localizable

The Bisognano–Wichmann Property on Nets of Standard Subspaces, Some Sufficient Conditions

Relative entanglement entropy for widely separated regions in curved spacetime

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