Algebraic Quantum Field Theory and Causal Symmetric Spaces

Neeb KH, Ólafsson G (2023)


Publication Type: Book chapter / Article in edited volumes

Publication year: 2023

Publisher: Springer Science and Business Media Deutschland GmbH

Edited Volumes: Geometric Methods in Physics XXXIX. WGMP 2022

Series: Trends in Mathematics

Book Volume: Part F1183

Pages Range: 207-231

DOI: 10.1007/978-3-031-30284-8_20

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.

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APA:

Neeb, K.-H., & Ólafsson, G. (2023). Algebraic Quantum Field Theory and Causal Symmetric Spaces. In Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (Eds.), Geometric Methods in Physics XXXIX. WGMP 2022. (pp. 207-231). Springer Science and Business Media Deutschland GmbH.

MLA:

Neeb, Karl-Hermann, and Gestur Ólafsson. "Algebraic Quantum Field Theory and Causal Symmetric Spaces." Geometric Methods in Physics XXXIX. WGMP 2022. Ed. Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T., Springer Science and Business Media Deutschland GmbH, 2023. 207-231.

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