2022-12-02T07:19:26Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000284482022-08-09T01:21:33ZFree products in AQFTLongo, RobertoTanimoto, YohUeda, Yoshimichiopen accessCet article est mis à disposition selon les termes de la licence Creative Commons attribution – pas de modification 3.0 France. http://creativecommons.org/licenses/by-nd/3.0/fr/Algebraic QFThalf-sided modular inclusionsconformal netsfree productsWe 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 ergodic canonical endomorphism, we obtain a half-sided modular inclusion with ergodic canonical endomorphism and trivial relative commutant. On the other hand, if we take Möbius covariant nets with trace class property, we are able to construct an inclusion of free product von Neumann algebras with large relative commutant, by considering either a finite family of identical inclusions or an infinite family of inequivalent inclusions. In two dimensional spacetime, we construct Borchers triples with trivial relative commutant by taking free products of infinitely many, identical Borchers triples. Free products of finitely many Borchers triples are possibly associated with Haag–Kastler net having S-matrix which is nontrivial and non asymptotically complete, yet the nontriviality of double cone algebras remains open.Centre Mersenne, Annales de l'Institut Fourier2019-06engjournal articleVoRhttp://hdl.handle.net/2237/00030639https://nagoya.repo.nii.ac.jp/records/28448https://doi.org/10.5802/aif.32691777-5310Annales de l'Institut Fourier69312291258https://nagoya.repo.nii.ac.jp/record/28448/files/AIF_2019__69_3_1229_0.pdfapplication/pdf3.2 MB2019-09-02