2024/07/30 by Maria Stella Adamo, Adamo, Maria Stella, Karl‐Hermann Neeb +3 · 1 citation
Engineering · Mathematics · #22E45 #43A35 #47B32 #47B91 #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #Operator Algebras (math.OA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2407.21123
openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a novel perspective on reflection positivity (RP) 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.