Algebraic Quantum Field Theory and causal homogeneous spaces - Part 2a/4 | Vidéo

Algebraic Quantum Field Theory and causal homogeneous spaces - Part 2a/4

Appears in collection : 2025 - T1 - Representation theory and noncommutative geometry

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.