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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: QFT in Curved Spacetimes

MP 2.1: Hauptvortrag

Dienstag, 20. März 2018, 11:00–11:45, Z6 - SR 1.012

Analytic Hadamard states and Wick rotation on curved spacetimes — •Christian Gérard — Laboratoire de Mathématiques Université Paris-Sud France

Hadamard states are substitutes for vacuum states when one considers for example a free Klein-Gordon field on a globally hyperbolic spacetime. Nowadays Hadamard states are caracterized microlocally by the wavefront set of their two-point function.

If the spacetime is analytic, one can define analytic Hadamard states, obtained using the analytic version of wavefront set, instead of the C^∞ version.

Analytic Hadamard states have the important Reeh-Schlieder property, which means that vectors obtained by acting on the ground state with fields localized in any fixed region of spacetime are dense in the physical Hilbert space.

So far the existence of analytic Hadamard states is known only in the very simple situation of static spacetimes. In this talk I will explain a construction of analytic Hadamard states on any analytic spacetime having an analytic Cauchy surface.

The proof uses the Wick rotation in Gaussian normal coordinates and a well-known tool from elliptic boundary value problems, called the Calderon projectors.