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

@inproceedings{Gerard2021HadamardSF, title={Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry}, author={Christian G'erard and Th'eo Stoskopf}, year={2021} }

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.

## 3 Citations

M{\o}ller operators and Hadamard states for Dirac fields with MIT boundary conditions

- Physics, Mathematics
- 2021

The aim of this paper is to prove the existence of Hadamard states for Dirac fields coupled with MIT boundary conditions on any globally hyperbolic manifold with timelike boundary. This is achieved…

Paracausal deformations of Lorentzian metrics and M{\o}ller isomorphisms in algebraic quantum field theory

- Physics, Mathematics
- 2021

Given a pair of normally hyperbolic operators over (possibily different) globally hyperbolic spacetimes on a given smooth manifold, the existence of a geometric isomorphism, called Møller operator,…

Hadamard property of the in and out states for Dirac fields on asymptotically static spacetimes

- Mathematics, Physics
- 2021

We consider massive Dirac equations on asymptotically static spacetimes with a Cauchy surface of bounded geometry. We prove that the associated quantized Dirac field admits in and out states, which…

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