Thermal States in Conformal QFT. I |
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Authors: | Paolo Camassa Roberto Longo Yoh Tanimoto Mihály Weiner |
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Institution: | (1) Fachbereich 3, Mathematik und Informatik, Universit?t Bremen, Bibliothekstrasse 1, 28359 Bremen, Germany;(2) Institut f?r Mathematische Stochastik, Maschm?hlenweg 8-10, 37073 G?ttingen, Germany;(3) Mathematical Institute, University of St. Andrews, North Haugh, St Andrews, KY, 16 9SS, Scotland |
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Abstract: | We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A{{\mathcal A}} of von Neumann algebras on
\mathbb R{\mathbb R} . In this first part, we focus on the completely rational net A{{\mathcal A}} . Our main result here states that, if A{{\mathcal{A}}} is completely rational, there exists exactly one locally normal KMS state j{\varphi} . Moreover, j{\varphi} is canonically constructed by a geometric procedure. A crucial r?le is played by the analysis of the “thermal completion
net” associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local
conformal nets w.r.t. the time-translation one-parameter group. |
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