Dirac Quantum Field on Curved Spacetime: Wick Rotation

TL;DR

This paper demonstrates the analytic continuation of Dirac field Green functions between Lorentzian and Euclidean signatures on curved spacetime, including at finite temperature, facilitating quantum field theory calculations.

Contribution

It provides a rigorous method for Wick rotation of Dirac fields on curved spacetime, extending previous flat spacetime results to more general geometries.

Findings

Successfully performs Wick rotation for Dirac fields on curved spacetime.

Establishes analytic continuation of Green functions at finite temperature.

Bridges Lorentzian and Euclidean quantum field theories in curved backgrounds.

Abstract

For a linear Dirac field on a globally hyperbolic static space-time the analytic continuation of its Wightman functions (Green functions) to Schwinger functions and back at zero and finite temperature is shown.