On Padmanabhan's duality invariance and the quantum of length

We provide a field–theoretic construction of Padmanabhan’s duality–invariant Feynman propagator for a massive point particle in Euclidean space [Formula: see text]. Padmanabhan’s propagator includes quantum–gravity effects due to the existence of a quantum of length [Formula: see text]. Including [Formula: see text] corrections, the corresponding field–theory model turns out to be a free, massive scalar defined in [Formula: see text]. The two additional dimensions with respect to the original [Formula: see text] provide the necessary room, so to speak, for quantum–gravity fluctuations.