  An outline is given of a recently discovered technique for building a quantum
effective action that is completely independent of gauge-fixing choices and
ghost determinants. One makes maximum use of the geometry and fibre-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 {\it et 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.
