Representation Theory and Noncommutative Geometry, Paris

Mini-course: Algebraic Quantum Field Theory and causal homogeneous spaces 3/4 (pt.1)

19 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 3: Analytic continuation of orbit maps and crown domains.

The construction of interesting nets of real subspaces rests on the existence of holomorphic extension of orbit maps in unitary representations. For semisimple groups, complex crowns of Riemannian symmetric spaces $G/K$ provide a natural context for this extension process. We explain how this can be set up on general Lie groups whose Lie algebra contains an Euler element.

Lecture notes are available under:
https://en.www.math.fau.de/wp-content/uploads/sites/3/2025/03/qft-lect.pdf