Representation Theory and Noncommutative Geometry, Paris

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

21 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 4: Constructing nets of real subspaces.

Finally, we arrive at rather general characterizations of unitary representations and homogeneous spaces for which a rich supply of nets exists. Many classification results are still open and more bridges to Physics have to be built, but the overall structure of the theory takes shape.

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