MG14 - Talk detail

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Existence of Hadamard states for a free field theory on a globally hyperbolic spacetime is proven via an old deformation argument, proposed by Fulling, Narkowich and Wald in the eighties. The main deficiency of this scheme is the complete loss of any control on the invariance of the state under the action of the background isometries. In order to account for them, one needs to resort to specific construction schemes which are often valid for a given free field with a fixed value of the mass and, if present, of the coupling to scalar curvature. Via an improved version of the Moller operator, we show that, these isometry invariant Hadamard states can be deformed to Hadamard states for any value of the mass and of the coupling to scalar curvature. Furthermore the invariance under any spacelike isometry is preserved, while, for the timelike ones, a sort of adiabatic procedure is necessary. We comment on the latter in the last part of the talk. Joint work with Nicolò Drago (U. of Genoa)

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