Free products in AQFT
Abstract
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 halfsided modular inclusions with ergodic canonical endomorphism, we obtain a halfsided 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 HaagKastler net having Smatrix which is nontrivial and non asymptotically complete, yet the nontriviality of double cone algebras remains open.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 DOI:
 10.48550/arXiv.1706.06070
 arXiv:
 arXiv:1706.06070
 Bibcode:
 2017arXiv170606070L
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Operator Algebras;
 81T05;
 46L54;
 81T40
 EPrint:
 23 pages, no figure