  We discuss several aspects of second quantized scattering operators $\hat S$
for fermions in external time dependent fields. We derive our results on a
general, abstract level having in mind as a main application potentials of the
Yang--Mills type and in various dimensions. We present a new and powerful
method for proving existence of $\hat S$ which is also applicable to other
situations like external gravitational fields. We also give two complementary
derivations of the change of phase of the scattering matrix under generalized
gauge transformations which can be used whenever our method of proving
existence of $\hat S$ applies. The first is based on a causality argument i.e.\
$\hat S$ (including phase) is determined from a time evolution, and the second
exploits the geometry of certain infinite-dimensional group extensions
associated with the second quantization of 1-particle operators. As a special
case we obtain a Hamiltonian derivation of the the axial Fermion-Yang-Mills
anomaly and the Schwinger terms related to it via the descent equations, which
is on the same footing and traces them back to a common root.
