Singularity structure of the two point function of the free Dirac field on a globally hyperbolic spacetime

TL;DR

This paper reviews microlocal analysis techniques used to study the singularity structure of two-point functions in free quantum fields on curved spacetimes, focusing on the Dirac and Klein-Gordon fields.

Contribution

It introduces the polarization set of the Hadamard two-point function for the free Dirac field on curved spacetimes, extending previous microlocal analysis methods.

Findings

Calculation of the wave front set for Klein-Gordon fields in Hadamard states

Determination of the polarization set for Dirac fields

Enhanced understanding of singularity structures in quantum field theory on curved spacetime

Abstract

We give an introduction to the techniques from microlocal analysis that have successfully been applied in the investigation of Hadamard states of free quantum field theories on curved spacetimes. The calculation of the wave front set of the two point function of the free Klein-Gordon field in a Hadamard state is reviewed, and the polarization set of a Hadamard two point function of the free Dirac field on a curved spacetime is calculated.