Spacetime metric from quantum-gravity corrected Feynman propagators

TL;DR

This paper investigates how quantum-gravity corrections to Feynman propagators, modeled via a zero-point length, influence the derived spacetime metric, confirming that classical metrics are recovered at scales larger than the quantum length.

Contribution

It introduces a method to derive spacetime metrics from quantum-gravity corrected Feynman propagators and verifies their consistency with classical metrics at large scales.

Findings

Quantum-gravity corrections modify the Feynman propagator by a zero-point length.

Derived metrics from corrected propagators match classical metrics at distances greater than L.

The analysis is performed in Euclidean flat spacetime.

Abstract

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length $L>0$. These corrections cause the length element $\sqrt{s^2}$ to be replaced with $\sqrt{s^2 + 4L^2}$ within the Feynman propagator. In this paper we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length $L$. We perform this analysis in the case of the background spacetime $\mathbb{R}^D$ in the Euclidean sector.