Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry

Abstract

We consider Dirac equations on even-dimensional Lorentzian manifolds of bounded geometry with a spin structure. For the associated free quantum field theory, we construct pure Hadamard states using global pseudodifferential calculus on a Cauchy surface. We also give two constructions of Hadamard states for Dirac fields for arbitrary spacetimes with a spin structure.