Construction of Hadamard states by pseudo-differential calculus

Christian Gérard (1) , Michal Wrochna (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 MAUG - Mathematisches Institut Universitat Goettingen

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.

Mots clés: Hadamard states; microlocal spectrum condition; pseudo-differential calculus

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Christian Gérard, Michal Wrochna. Construction of Hadamard states by pseudo-differential calculus. 2012. ⟨hal-00731137v1⟩