Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
133 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Reflection positivity and its relation to disc, half plane and the strip (2407.21123v1)

Published 30 Jul 2024 in math.FA, math.OA, and math.RT

Abstract: 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 M\"obius 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 $H\infty$ 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.

Citations (1)

Summary

We haven't generated a summary for this paper yet.