Representation Theory and Noncommutative Geometry, Paris

Mini-course: Algebraic Quantum Field Theory and causal homogeneous spaces 2/4 (pt.1)

18 mars 2025, 10:00

45m

Amphitheater Darboux (IHP)

Orateur

Karl-Hermann Neeb (Friedrich-Alexander-University Erlangen-Nuremberg)

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