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

@article{Lechner2021DeformationsOH,
  title={Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories},
  author={Gandalf Lechner and Charley Scotford},
  journal={Communications in Mathematical Physics},
  year={2021},
  volume={391},
  pages={269 - 291}
}
We construct explicit examples of half-sided modular inclusions N⊂M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N}\subset \mathcal {M}$$\end{document} of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms of an… 

Modular Structure and Inclusions of Twisted Araki-Woods Algebras

. In the general setting of twisted second quantization (including Bose/Fermi second quantization, S -symmetric Fock spaces, and full Fock spaces from free probability as special cases), von Neumann

Fermionic integrable models and graded Borchers triples

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

References

SHOWING 1-10 OF 42 REFERENCES

Half-Sided modular inclusions of von-Neumann-Algebras

AbstractLetN ⊂M be von-Neumann-Algebras on a Hilbert spaceH, Ω a common cyclic and separating vector. Denote ΔM,ΔN resp. JM,JN the associated modular operators and conjugations. Assume ΔM-it,ΔN+it ⊂N

An Algebraic Construction of Boundary Quantum Field Theory

We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras $${\mathcal A_V}$$ on the Minkowski half-plane M+ starting with a local conformal net

Extensions of Conformal Nets¶and Superselection Structures

Abstract:Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Möbius group. We infer from this

Wedge domains in compactly causal symmetric spaces

Motivated by construction in Algebraic Quantum Field Theory we introduce wedge domains in compactly causal symmetric spaces M = G/H , which includes in particular anti de Sitter space in all

Free products in AQFT

We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with

On the failure of microcausality in noncommutative field theories

We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking $O(x)=:\phi\star\phi:(x)$ as a sample observable. Using methods of the theory of

Wedge-Local Quantum Fields and Noncommutative Minkowski Space

Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski space, the consequences of the consistent application of the proper, untwisted Poincare group as the

Construction of Wedge-Local Nets of Observables Through Longo-Witten Endomorphisms

A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scattering matrix

Antiunitary representations and modular theory

Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a

Lightfront Formalism versus Holography&Chiral Scanning

The limitations of the approach based on using fields restricted to the lightfront (Lightfront Quantization or p$\to \infty $ Frame Approach) which drive quantum fields towards canonical and