Exact Results in Quantum Theory

I review the locally gauge covariant formulation of QFT in background gauge fields, which is a generalization of the locally covariant framework for QFT on curved space-times. The principle of perturbative agreement, introduced by Hollands & Wald, is applied to gauge background fields and a form of the Adler-Bardeen theorem is derived. Finally, these concepts are applied to a discussion of global anomalies. The latter part is based on joint work with A. Schenkel.