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Using properties of the determinant line bundle for a family of ellipticboundary value problems, we explain how the Fock space functor defines anaxiomatic quantum field theory which formally models the Fermionic pathintegral. The 'sewing axiom' of the theory arises as an algebraic pasting lawfor the determinant of the Dirac operator. We show how representations of theboundary gauge group fit into this description and that this leads to a Fockfunctor description of certain gauge anomalies.Comment: 40 pages (latex

Functorial QFT, Gauge Anomalies¶and the Dirac Determinant Bundle