Vincenzo Morinelli
From local nets to Euler elements
The interplay between geometric and algebraic structures in Algebraic Quantum Field Theory (AQFT) has long been a rich field of study, drawing insights from operator algebras, Lie theory, category theory, and other areas of mathematics. An important theme in AQFT is understanding how the localization properties and the properties of local algebras of quantum fields are tied to the underlying geometry of the models. In recent joint work with K.-H. Neeb (University of Erlangen-Nürnberg), we have studied this relationship through the Lie theory language, to generalize geometric-algebraic correspondences within AQFT. We will discuss the deep relationship between the geometry of standard subspaces, the geometry of Euler elements in the Lie algebra of a Lie group and the geometry of an Algebraic Quantum Field Theory. We will also present the construction and the properties of new geometric models that we have developed within a generalized framework for AQFT.
Based on the joint work with K.-H., "From local nets to Euler elements", Advances in Mathematics, Volume 458, Part A, (2024).
