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.
Communications in Mathematical Physics
- Pub Date:
- January 2014
- Mathematical Physics;
- Mathematics - Analysis of PDEs
- Final version. Discussion of Hadamard condition and of charge reversal expanded