Wick rotation and the positivity of energy in quantum field theory

TL;DR

This paper introduces a new axiom system for quantum field theories on curved spacetimes, emphasizing the analytic extension of partition functions and correlators to complex metrics, bridging Riemannian and Lorentzian geometries.

Contribution

It proposes a novel axiomatic framework that unifies Riemannian and Lorentzian metrics through analytic continuation in quantum field theory.

Findings

Partition functions extend analytically to complex metrics.

Riemannian metrics are within the domain, Lorentzian on the boundary.

Provides a new perspective on energy positivity in QFT.

Abstract

We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary Riemannian metrics are contained in the allowable domain, while Lorentzian metrics lie on its boundary.