Revisiting the minimum length in the Schwinger–Keldysh formalism

The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger–Keldysh for- malism. No minimum geometrical length is found for arbi- trary gravitational theories to all orders in perturbation the- ory. Using non-perturbative techniques, we also show that neither the conformal sector of general relativity nor higher- derivative gravity features a minimum length. A minimum length scale, on the other hand, seems to always be present when one considers in-out amplitudes, from which one could extract the energy scale of scattering processes.