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arXiv · 1411.2439

Reflection positivity for the circle group

Karl-Hermann Neeb·Gestur Olafsson
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Abstract

In this note we characterize those unitary one-parameter groups U^c which admit euclidean realizations in the sense that they are obtained by the analytic continuation process corresponding to reflection positivity from a unitary representation $U$ of the circle group. These are precisely the ones for which there exists an anti-unitary involution $J$ commuting with $U^c$. This provides an interesting link with the modular data arising in Tomita--Takesaki theory. Introducing the concept of a positive definite function with values in the space of sesquilinear forms, we further establish a link between KMS states and reflection positivity on the circle.

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Karl-Hermann Neeb, Gestur Olafsson. 2014-11-10. Reflection positivity for the circle group. https://doi.org/10.1088/1742-6596%2F597%2F1%2F012004

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