Group cocycles, line bundles, and anomalies

The relation between complex line bundles and certain group cocycles is explored in general to obtain explicit formulae for the transition functions and curvature of the determinant line bundle DET of a family of Dirac operators coupled to Yang-Mills fields. A covariant derivative on sections of DET is constructed which realizes the curvature and 'minimally couples' to the integrated anomaly which thus appears as a 'functional magnetic field' on gauge orbit space. The transcription of group cohomological (cocycles) into geometrical (line bundles) information is refined in such a way that the relevant cohomology groups can be computed in many cases, giving insight into the classification of lifts of principal group actions. 23 refs. (Author)