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Analytic Hadamard States, Calderón Projectors and Wick Rotation Near Analytic Cauchy Surfaces

  • Christian Gérard
  • Michał WrochnaEmail author
Article
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Abstract

We consider the Klein–Gordon equation on analytic spacetimes with an analytic Cauchy surface. In this setting, we prove the existence of pure analytic Hadamard states. The proof is based on considering an elliptic operator obtained by Wick rotating the Klein–Gordon operator in a neighborhood of a Cauchy hypersurface. The Cauchy data of Hadamard two-point functions are constructed as Calderón projectors (suitably generalized if the hypersurface is non-compact) for the elliptic operator.

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Acknowledgements

The authors would like to thank Pierre Schapira for all the useful discussions. Support from the Grants ANR-12-BS01-012-01 and ANR-16-CE40-0012-01 is gratefully acknowledged.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Paris-Sud XIOrsay CedexFrance
  2. 2.CNRS, Institut FourierUniversité Grenoble AlpesGrenobleFrance

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