Chiral anomalies, higher dimensions, and differential geometry

We determine the abelian and non-abelian chiral anomalies in 2n-dimensional spacetime by a differential geometric method which enables us to obtain the anomalies without having to calculate Feynman diagrams, as has been done by Frampton and Kephart. The advantage of this method is that the construction automatically satisfies the Wess-Zumino consistency condition, a condition which has direct physical interpretation. We hope that our analysis sheds light on the mathematical structure associated with ciral anomalies. The mathematical analysis is self-contained and a brief review of differential forms and other mathematical tools is included. (orig.)