Würzburg Seminar on Quantum Field Theory and Gravity

Quantum entanglement is usually defined after choosing a fixed tensor-product decomposition of a Hilbert space. In this talk I will explain a different viewpoint, in which entanglement is treated as a global geometric phenomenon. When a quantum system varies over a parameter space, the local state spaces may look identical, yet their global gluing can be twisted. Then a consistent notion of subsystems—and with it a global distinction between product and entangled states— may fail to exist. I will describe how this problem is formulated using Azumaya algebras and Severi-Brauer schemes, and how familiar notions such as product states and Schmidt rank acquire a geometric meaning. This viewpoint also suggests new universal effects, including holonomy induced entangling phenomena beyond the usual Berry phase and Chern number framework. I will conclude with applications to condensed matter theory and broader connections among tensor geometry, representation theory, and topological materials.