Reflection positivity and its relation to disc, half plane and the strip

Adamo MS, Neeb KH, Schober J (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Expositiones Mathematicae Elsevier

Book Volume: 43

Article Number: 125660

Journal Issue: 4

DOI: 10.1016/j.exmath.2025.125660

Abstract

We present a novel perspective on reflection positivity on the strip by systematically developing the analogies with the unit disc and the upper half plane in the complex plane. These domains correspond to the three conjugacy classes of one-parameter groups in the Möbius group (elliptic for the disc, parabolic for the upper half plane and hyperbolic for the strip). In all cases, reflection positive functions correspond to positive functionals on H∞ for a suitable involution. For the strip, reflection positivity naturally connects with Kubo–Martin–Schwinger (KMS) conditions on the real line and further to standard pairs, as they appear in Algebraic Quantum Field Theory. We also exhibit a curious connection between Hilbert spaces on the strip and the upper half plane, based on a periodization process.

Authors with CRIS profile

Maria Stella Adamo Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie) Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

National Autonomous University of Mexico / Universidad Nacional Autónoma de México (UNAM) MX Mexico (MX)

How to cite

APA:

Adamo, M.S., Neeb, K.H., & Schober, J. (2025). Reflection positivity and its relation to disc, half plane and the strip. Expositiones Mathematicae, 43(4). https://doi.org/10.1016/j.exmath.2025.125660

MLA:

Adamo, Maria Stella, Karl Hermann Neeb, and Jonas Schober. "Reflection positivity and its relation to disc, half plane and the strip." Expositiones Mathematicae 43.4 (2025).

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