Reflection positivity for the circle group
Neeb KH, Olafsson G (2015)
Publication Type: Journal article, Original article
Publication year: 2015
Journal
Publisher: Institute of Physics: Open Access Journals / Institute of Physics (IoP)
Book Volume: 597
Article Number: 012004
DOI: 10.1088/1742-6596/597/1/012004
Abstract
In this note we characterize those unitary one-parameter groups (Uct)t2R which admit euclidean realizations in the sense that they are obtained by the analytic continuation process corresponding to re ection 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 Uc. This provides an interesting link with the modular data arising in Tomita{Takesaki theory.
Introducing the concept of a positive de nite function with values in the space of sesquilinear
forms, we further establish a link between KMS states and re ection positivity on the circle.
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APA:
Neeb, K.H., & Olafsson, G. (2015). Reflection positivity for the circle group. Journal of Physics : Conference Series, 597. https://dx.doi.org/10.1088/1742-6596/597/1/012004
MLA:
Neeb, Karl Hermann, and Gestur Olafsson. "Reflection positivity for the circle group." Journal of Physics : Conference Series 597 (2015).
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