Some Generalized BRS Transformations.I The Pure Yang-Mills Case

Some generalized BRS transformations are developed for the pure Yang-Mills theory, and a form of quantum gravity. Unlike the usual BRS transformations: these are nonlocal; may be infinite formal power series in the gauge fields; and do not leave the action invariant, but only the product exp(-S) with the Jacobian. Similar constructions should exist for many other field theory situations.