Quantum gravity without ghosts

We give an outline of a recently discovered technique for building quantum effective action that is completely independent of gauge-fixing choices and ghost determinants. One makes maximum use of the geometry and fiber bundle structure of the space of field histories and introduces a set of nonlocal composite fields: the geodesic normal fields based on Vilkovisky's connection on the space of histories. The closed-time-path formalism of Schwinger, Bakshi, Mahantappa ct al. can be adapted for these fields, and a set of gauge-fixing-independent dynamical equations for their expectation values (starting from given initial conditions) can be computed. An obvious application for such equations is to the study of the formation and radiative decay of black holes, and to other back-reaction problems.