  Many field theories of physical interest have configuration spaces consisting
of disconnected components. Quantum mechanical amplitudes are then expressed as
sums over these components. We use the Faddeev-Popov approach to write the
terms in this topological expansion as moduli space integrals. A cut-off is
needed when these integrals diverge. This introduces a dependence on the choice
of parametrisation of configuration space which must be removed if the theory
is to make physical sense. For theories that have a local symmetry this also
leads to a breakdown in BRST invariance. We discuss in detail the cases of
Bosonic Strings and Yang-Mills theory, showing how this arbitrariness may be
removed by the use of a counter-term in the former case, and by
compactification on $S\sp 4$ in the latter.
