  For quantum field theories with topological sectors, Monte Carlo simulations
on fine lattices tend to be obstructed by an extremely long auto-correlation
time with respect to the topological charge. Then reliable numerical
measurements are feasible only within individual sectors. The challenge is to
assemble such restricted measurements in a way that leads to a substantiated
approximation to the fully fledged result, which would correspond to the
correct sampling over the entire set of configurations. We test an approach for
such a topological summation, which was suggested by Brower, Chandrasekharan,
Negele and Wiese. Under suitable conditions, energy levels and susceptibilities
can be obtained to a good accuracy, as we demonstrate for O(N) models, SU(2)
Yang-Mills theory, and for the Schwinger model.
