  Using properties of the determinant line bundle for a family of elliptic
boundary value problems, we explain how the Fock space functor defines an
axiomatic quantum field theory which formally models the Fermionic path
integral. 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 Fock
functor description of certain gauge anomalies.
