On revolutionizing quantum field theory with Tomita's modular theory

HJ Borchers - Journal of mathematical Physics, 2000 - pubs.aip.org
In the book of Haag [Local Quantum Physics (Springer Verlag, Berlin, 1992)] about local
quantum field theory the main results are obtained by the older methods of C*-and W …

Modular localization and Wigner particles

R Brunetti, D Guido, R Longo - Reviews in Mathematical Physics, 2002 - World Scientific
We propose a framework for the free field construction of algebras of local observables
which uses as an input the Bisognano–Wichmann relations and a representation of the …

Multi-interval subfactors and modularity¶ of representations in conformal field theory

Y Kawahigashi, R Longo, M Müger - Communications in Mathematical …, 2001 - Springer
We describe the structure of the inclusions of factors?(E)⊂?(E′)′ associated with multi-
intervals E⊂ ℝ for a local irreducible net? of von Neumann algebras on the real line …

Classification of local conformal nets. Case c< 1

Y Kawahigashi, R Longo - Annals of mathematics, 2004 - JSTOR
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the
circle with central charge c less than 1. The irreducible ones are in bijective correspondence …

Covariant homogeneous nets of standard subspaces

V Morinelli, KH Neeb - Communications in Mathematical Physics, 2021 - Springer
Rindler wedges are fundamental localization regions in AQFT. They are determined by the
one-parameter group of boost symmetries fixing the wedge. The algebraic canonical …

[HTML][HTML] From local nets to Euler elements

V Morinelli, KH Neeb - Advances in Mathematics, 2024 - Elsevier
Various aspects of the geometric setting of Algebraic Quantum Field Theory (AQFT) models
related to representations of the Poincaré group can be studied for general Lie groups …

Wightman fields for two-dimensional conformal field theories with pointed representation category

MS Adamo, L Giorgetti, Y Tanimoto - Communications in Mathematical …, 2023 - Springer
Two-dimensional full conformal field theories have been studied in various mathematical
frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our …

Topological sectors and a dichotomy in conformal field theory

R Longo, F Xu - Communications in mathematical physics, 2004 - Springer
Let be a local conformal net of factors on S 1 with the split property. We provide a topological
construction of soliton representations of the n-fold tensor product that restrict to true …

Conformal subnets and intermediate subfactors

R Longo - Communications in mathematical physics, 2003 - Springer
Given an irreducible local conformal net 𝒜 of von Neumann algebras on S 1 and a finite-
index conformal subnet ℬ⊂ 𝒜, we show that 𝒜 is completely rational iff ℬ is completely …

Antiunitary representations and modular theory

KH Neeb, G Ólafsson - arxiv preprint arxiv:1704.01336, 2017 - arxiv.org
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 …