Reflection Positivity on the Circle

  • Karl-Hermann NeebEmail author
  • Gestur Ólafsson
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 32)


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 \(\mathscr {S}_\beta := \{ z \in {\mathbb {C}}: 0< \mathop {\mathrm{Im}}\nolimits z < \beta \}.\)

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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