Construction of Hadamard States by Pseudo-Differential Calculus |
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Authors: | C Gérard M Wrochna |
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Institution: | 1. Département de Mathématiques, Université de Paris XI, 91405, Orsay Cedex, France 2. Mathematisches Institut, Universit?t G?ttingen, Bunsenstr. 3-5, 37073, G?ttingen, Germany
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Abstract: | 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 on this class of space-times, we construct all pure Hadamard states whose two-point function (expressed in terms of Cauchy data on a Cauchy surface) is a matrix of pseudo-differential operators. We also study their covariance under symplectic transformations. As an aside, we give a new construction of Hadamard states on arbitrary globally hyperbolic space-times which is an alternative to the classical construction by Fulling, Narcowich and Wald. |
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