  One-loop quantities in QFT can be computed in an efficient way using the
worldline formalism. The latter rests on the ability of calculating 1D path
integrals on the circle. In this paper we give a systematic discussion for
treating zero modes on the circle of 1D path integrals for both bosonic and
supersymmetric nonlinear sigma models, following an approach originally
introduced by Friedan. We use BRST techniques and place a special emphasis on
the issue of reparametrization invariance. Various examples are extensively
analyzed to verify and test the general set-up. In particular, we explicitly
check that the chiral anomaly, which can be obtained by the semiclassical
approximation of a supersymmetric 1D path integral, does not receive higher
order worldline contributions, as implied by supersymmetry.
