One-loop quantum gravity from a worldline viewpoint

We develop a worldline approach to quantum gravity in D =4. Using the background field method we consider the covariantly gauge fixed Einstein-Hilbert action with cosmological constant, and find a worldline representation of the differential operators identified by its quadratic approximation. We test it by computing the correct one-loop divergencies. Alternative worldline methods, such as the use of the O(4) spinning particle that is known to describe correctly the propagation of a massless spin 2 particle in D = 4, find obstructions in the coupling to an arbitrary background metric, apparently preventing a more extensive use in perturbative descriptions of quantum gravity. We expect that our model might simplify calculations of one-loop amplitudes with respect to standard quantum field theoretical methods.