10 papers
Orthogonal pairs of Euler elements II: Geometric Bisognano--Wichmann and Spin--Statistics Theorems
Vincenzo Morinelli, Karl-Hermann Neeb, Gestur Olafsson
Models in Algebraic Quantum Field Theory (AQFT) may be generalized including Lie groups of symmetries whose Lie algebras admit an Euler element , characterized by the property t…
Infinite-Dimensional Lie Groups
Helge Gloeckner, Karl-Hermann Neeb
This is a preliminary version of a book on infinite-dimensional Lie groups. It covers the basics of calculus and manifolds in the context of locally convex spaces, based on Bastian…
A classification of coadjoint orbits carrying Gibbs ensembles
Karl-Hermann Neeb
A coadjoint orbit of a Lie group is said to carry a Gibbs ensemble if the set of all , for which the function $α\mapsto e^…
Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory
Karl-Hermann Neeb
In these notes, we describe an interesting connection between unitary representations of Lie groups and nets of local algebras, as they appear in Algebraic Quantum Field Theory (AQ…
Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality
Vincenzo Morinelli, Karl-Hermann Neeb, Gestur Olafsson
The current article continues our project on representation theory, Euler elements, causal homogeneous spaces and Algebraic Quantum Field Theory (AQFT). We call a pair (h,k) of Eul…
Crowned Lie groups and nets of real subspaces
Daniel Beltita, Karl-Hermann Neeb
We introduce the notion of a complex crown domain for a connected Lie group , and we use analytic extensions of orbit maps of antiunitary representations to these domains to con…