Construction of Hadamard States by PseudoDifferential Calculus
Abstract
We give a new construction based on pseudodifferential calculus of quasifree Hadamard states for KleinGordon equations on a class of spacetimes whose metric is wellbehaved at spatial infinity. In particular on this class of spacetimes, we construct all pure Hadamard states whose twopoint function (expressed in terms of Cauchy data on a Cauchy surface) is a matrix of pseudodifferential operators. We also study their covariance under symplectic transformations. As an aside, we give a new construction of Hadamard states on arbitrary globally hyperbolic spacetimes which is an alternative to the classical construction by Fulling, Narcowich and Wald.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 January 2014
 DOI:
 10.1007/s0022001318249
 arXiv:
 arXiv:1209.2604
 Bibcode:
 2014CMaPh.325..713G
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 Final version. Discussion of Hadamard condition and of charge reversal expanded