Year: 2015
Type: conference-paper
Abstract: In this note we characterize those unitary one-parameter groups ( U t c ) 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 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.
Authors: K-H Neeb, G Ólafsson
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2105271981