Speaker
Description
Models in Algebraic Quantum Field Theory can be generalized to include Lie group symmetries whose Lie algebras admit an Euler element h, characterized by the property that ad h is diagonalizable with eigenvalues in {−1,0,1}. These elements become relevant to the formal description of wedge localization.
Within the geometric framework established in previous works with K.-H. Neeb and G. Ólafsson, we derive both a Bisognano–Wichmann Theorem and a Spin–Statistics Theorem for nets of standard subspaces and von Neumann algebras. We will present the framework and the results, and compare them with those in the AQFT literature. A key role in our analysis is played by the structure of orthogonal Euler elements, namely pairs of Euler elements (h,k) in the Lie algebra such that e^{iπ ad h}(k) = −k, reflecting the geometry of boost generators in orthogonal directions in Minkowski space.
Based on the papers:
V. Morinelli K.-H. Neeb and G.Ólafsson, Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality, Forum Mathematicum (2025) and Orthogonal pairs of Euler elements II: Geometric Bisognano–Wichmann and Spin–Statistics Theorems, arXiv:2603.26390v1 (2026)