English

Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory

Operator Algebras 2025-11-13 v1 Mathematical Physics math.MP Representation Theory

Abstract

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 (AQFT). It is based on first translating the axioms for nets of operator algebras parameterized by regions in a space-time manifold into those for nets of real subspaces, and then study this structure from a perspective based on geometry and representation theory of Lie groups.

Keywords

Cite

@article{arxiv.2511.09360,
  title  = {Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory},
  author = {Karl-Hermann Neeb},
  journal= {arXiv preprint arXiv:2511.09360},
  year   = {2025}
}

Comments

168 pages; lecture notes