N-Particle Scattering in Relativistic Wedge-Local Quantum Field Theory

Duell, Maximilian

doi:10.1007/s00220-018-3183-z

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…For physical interpretations of such a light ray holography (in a somewhat different context), see for instance [Sch02]. It should also be noted that the deformed field theory (and related models, including models in higher dimensions) are interacting in the sense of having a non-trivial S-matrix; see [GL07] for two-particle scattering and [Due18,Due19] for an analysis of n-particle scattering.…”

Section: Two-dimensional Nets and Warped Convolutionmentioning

confidence: 99%

Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories

Lechner

Scotford

2022

Commun. Math. Phys.

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We construct explicit examples of half-sided modular inclusions $$\mathcal {N}\subset \mathcal {M}$$ N ⊂ M of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms of an algebra localized at infinity, we consider a second quantization inclusion $$\mathcal {N}\subset \mathcal {M}$$ N ⊂ M with large relative commutant and construct a one-parameter family $$\mathcal {N}_\kappa \subset \mathcal {M}_\kappa $$ N κ ⊂ M κ , $$\kappa \ge 0$$ κ ≥ 0 , of half-sided inclusions such that $$\mathcal {N}_0=\mathcal {N}$$ N 0 = N , $$\mathcal {M}_0=\mathcal {M}$$ M 0 = M and $$\mathcal {N}_\kappa '\cap \mathcal {M}_\kappa =\mathbb {C}1$$ N κ ′ ∩ M κ = C 1 for $$\kappa >0$$ κ > 0 . The technique we use is an explicit deformation procedure (warped convolution), and we explain the relation of this result to the construction of chiral conformal quantum field theories on the real line and on the circle.

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Section: Two-dimensional Nets and Warped Convolutionmentioning

confidence: 99%

Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories

Lechner

Scotford

2022

Commun. Math. Phys.

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“…To that end, we will follow the recent approach of Duell [Due18] to Haag-Ruelle scattering based on wedge-localized observables, specializing it to 1+1 space-time dimensions. We formulate it here directly for the case of Borchers triples, which comes with no loss of generality, since all 1+1-dimensional local nets which fulfill wedge duality (as assumed in [Due18]) arise from such triples [Bor92]. Also, we generalize the framework to the graded case, which is possible with minimal modifications.…”

Section: Scattering Theorymentioning

confidence: 99%

“…The proof is as in [Due18], in particular Theorem 6, Proposition 23, and Theorem 24 there, with the following changes: Apart from the easy addition of the relation for U (j) in (5.7), and trivial changes in notation, we have replaced M x with M t…”

Section: Scattering Theorymentioning

confidence: 99%

Fermionic integrable models and graded Borchers triples

Bostelmann¹,

Cadamuro²

2021

Preprint

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We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1 dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, altough it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag-Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme.

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Interacting Massless Infraparticles in 1+1 Dimensions

Dybalski

Mund

2022

Commun. Math. Phys.

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N-Particle Scattering in Relativistic Wedge-Local Quantum Field Theory

Cited by 4 publications

References 33 publications

Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories

Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories

Fermionic integrable models and graded Borchers triples

Interacting Massless Infraparticles in 1+1 Dimensions

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