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.