Spacetime metric from quantum-gravity corrected Feynman propagators

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 [Formula: see text]. These corrections cause the length element [Formula: see text] to be replaced with [Formula: see text] 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 [Formula: see text]. We perform this analysis in the case of the background spacetime [Formula: see text] in the Euclidean sector.