  The classical matter fields are sections of a vector bundle E with base
manifold M. The space L^2(E) of square integrable matter fields w.r.t. a
locally Lebesgue measure on M, has an important module action of C_b^\infty(M)
on it. This module action defines restriction maps and encodes the local
structure of the classical fields. For the quantum context, we show that this
module action defines an automorphism group on the algebra A, of the canonical
anticommutation relations on L^2(E), with which we can perform the analogous
localization. That is, the net structure of the CAR, A, w.r.t. appropriate
subsets of M can be obtained simply from the invariance algebras of appropriate
subgroups. We also identify the quantum analogues of restriction maps. As a
corollary, we prove a well-known "folk theorem," that the algebra A contains
only trivial gauge invariant observables w.r.t. a local gauge group acting on
E.
