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

TL;DR

This paper constructs pure Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry, using pseudodifferential calculus, and provides methods applicable to arbitrary spacetimes with spin structures.

Contribution

It introduces new constructions of Hadamard states for Dirac fields on Lorentzian manifolds, extending applicability to arbitrary spacetimes with spin structures.

Findings

Constructed pure Hadamard states using pseudodifferential calculus.

Extended constructions to arbitrary spacetimes with spin structures.

Published in Rev. Math. Phys.

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.(2nd revised version). Will appear in Rev. Math. Phys.