Title

Reflection positivity for the circle group

Document Type

Conference Proceeding

Publication Date

4-13-2015

Abstract

In this note we characterize those unitary one-parameter groups (Utc)t∈R 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 Uc. 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.

Publication Source (Journal or Book title)

Journal of Physics: Conference Series

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