Seminario de topología

Título: C*-categorical prefactorization algebras of superselection sectors

Ponente: Víctor Carmona (MPI, Leipzig)

Fecha: 22 de mayo (jueves) de 15:00 a 16:00.

Lugar: Aula 102 módulo 17

Abstract: A major result by Doplicher, Haag, and Roberts in algebraic quantum field theory shows that one can derive particle statistics from local quantum observables using first principles. While this may sound like a string of technical jargon, the core mathematical idea is neat: there exists a braided (or symmetric) monoidal category of superselection sectors—interpreted as charges or direct summands of the Hilbert space of states—that can be constructed entirely from the net of algebras of local observables. The statistics (i.e. what distinguishes bosons from fermions) of an irreducible sector can then be extracted from the action of the braid (or symmetric) group on tensor powers of that sector within the aforementioned category.

In this talk, we aim to introduce these ideas to the audience, assuming no prior background. We will also present a new construction of the braided monoidal category of superselection sectors for lattice quantum systems, employing tools from higher algebra. This is based on joint work with Benini, Naaijkens, and Schenkel [arXiv:2505.07960].