  A geometric formal method for perturbatively expanding functional integrals
arising in quantum gauge theories is described when the spacetime is a compact
riemannian manifold without boundary. This involves a refined version of the
Faddeev-Popov procedure using the covariant background field gauge-fixing
condition with background gauge field chosen to be a general critical point for
the action functional (i.e. a classical solution). The refinement takes into
account the gauge-fixing ambiguities coming from gauge transformations which
leave the critical point unchanged, resulting in the absence of infrared
divergences when the critical point is isolated modulo gauge transformations.
The procedure can be carried out using only the subgroup of gauge
transformations which are topologically trivial, possibly avoiding the usual
problems which arise due to gauge-fixing ambiguities. For Chern-Simons gauge
theory the method enables the partition function to be perturbatively expanded
for a number of simple spacetime manifolds such as $S^3$ and lens spaces, and
the expansions are shown to be formally independent of the metric used in the
gauge-fixing.
