Functorial QFT, gauge anomalies and the Dirac determinant bundle

Using properties of the determinant line bundle for a family of elliptic bo undary value problems, we explain how the Fock space functor defines an axi omatic quantum field theory which formally models the Fermionic path integr al. The "sewing axiom" of the theory arises as an algebraic pasting law for the determinant of the Dirac operator. We show how representations of the boundary gauge group fit into this description and that this leads to a Foc k functor description of certain gauge anomalies.