Abstract
In this chapter we turn to the close relation between reflection positivity on the circle group \({\mathbb T}\) and the Kubo–Martin–Schwinger (KMS) condition for states of \(C^*\)-dynamical systems. Here a crucial point is a pure representation theoretic perspective on the KMS condition formulated as a property of form-valued positive definite functions on \({\mathbb R}\): For \(\beta > 0\), we consider the open strip \(\mathscr {S}_\beta := \{ z \in {\mathbb {C}}: 0< \mathop {\mathrm{Im}}\nolimits z < \beta \}.\)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 The Author(s)
About this chapter
Cite this chapter
Neeb, KH., Ólafsson, G. (2018). Reflection Positivity on the Circle. In: Reflection Positivity. SpringerBriefs in Mathematical Physics, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-319-94755-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-94755-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94754-9
Online ISBN: 978-3-319-94755-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)