Fakultät für Physik und Astronomie

Würzburg Seminar on Quantum Field Theory and Gravity

A Type I Approximation of the Crossed Product
Datum: 28.11.2023, 14:45 - 15:45 Uhr
Ort: online
Veranstalter: Lehrstuhl für Theoretische Physik III
Vortragende: Ronak Soni (U. of Cambridge)

I show that an analog of the crossed product construction that takes type III1 algebras to type II algebras exists also in the type I case. This is particularly natural when the local algebra is a non-trivial direct sum of type I factors. Concretely, I rewrite the usual type I trace in a different way and renormalise it. This new renormalised trace stays well-defined even when each factor is taken to be type III. I am able to recover both type II as well as type II1 algebras by imposing different constraints on the central operator in the code. An example of this structure appears in holographic quantum error-correcting codes; the central operator is then the area operator.