Algebraic Quantum Field Theory and Causal Symmetric Spaces

Document Type

Article

Publication Date

1-1-2023

Abstract

In this chapter, we review our recent work on the causal structure of symmetric spaces and related geometric aspects of algebraic quantum field theory. Motivated by some general results on modular groups related to nets of von Neumann algebras, we focus on Euler elements of the Lie algebra, i.e., elements whose adjoint action defines a 3-grading. We study the wedge regions they determine in corresponding causal symmetric spaces and describe some methods to construct nets of von Neumann algebras on causal symmetric spaces that satisfy abstract versions of the Reeh–Schlieder and the Bisognano–Wichmann condition.

Publication Source (Journal or Book title)

Trends in Mathematics

First Page

207

Last Page

231

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