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Construction of Hadamard states by pseudo-differential calculus

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arxiv 1209.2604 v4 pith:566NJBJE submitted 2012-09-12 math-ph math.APmath.MP

Christian Gérard (LM-Orsay) , Micha{AA} Wrochna (MAUG) This is my paper · ORCID
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keywords hadamardstatesconstructioncalculusgivepseudo-differentialspace-timesarbitrary
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We give a new construction based on pseudo-differential calculus of quasi-free Hadamard states for Klein-Gordon equations on a class of space-times whose metric is well-behaved at spatial infinity. In particular we construct all pure Hadamard states and study their covariance under symplectic transformations. Using our results we give a new construction of Hadamard states on arbitrary globally hyperbolic space-times.

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