Speaker
Description
Lorentzian manifolds and their conformal compactifications provide the most symmetric models of spacetimes. The structures studied on such spaces in Algebraic Quantum Field Theory (AQFT) are so-called nets of operator algebras, i.e., to each open subset ${\mathcal O}$ of the space-time manifold one associates a von Neumann algebra ${\mathcal M}({\mathcal O})$ in such a way that a certain natural list of axioms is satisfied.
We report on an ongoing project concerned with the construction of such nets on general causal homogeneous spaces $M = G/H$.
Lecture 2: Euler elements and causal homogeneous spaces.
We explore which specific structures we need on the homogeneous space $M = G/H$ and the Lie group $G$, so that a rich supply of nets may exist. In particular, we explain how Euler elements of Lie algebras (elements defining 3-gradings) enter the picture as candidates of generators of modular groups. This leads to several families of causal homogeneous spaces such as compactly and non-compactly causal symmetric spaces and causal flag manifolds.
Lecture notes are available under:
https://en.www.math.fau.de/wp-content/uploads/sites/3/2025/03/qft-lect.pdf