  We present a model-independent method of dealing with fermion flavor mixing
in the case when instead of constant, momentum-independent mass matrices one
has rather momentum-dependent self-energies. This situation is typical for
strongly coupled models of dynamical fermion mass generation. We demonstrate
our approach on the example of quark mixing. We show that quark self-energies
with a generic momentum dependence lead to an effective
Cabibbo-Kobayashi-Maskawa (CKM) matrix, which turns out to be in general
non-unitary, in accordance with previous claims of other authors, and to
non-trivial flavor changing electromagnetic and neutral currents. We also
discuss some conceptual consequences of the momentum-dependent self-energies
and show that in such a case the interaction basis and the mass basis are not
related by a unitary transformation. In fact, we argue that the latter is
merely an effective concept, in a specified sense. While focusing mainly on the
fermionic self-energies, we also study the effects of momentum-dependent
radiative corrections to the gauge bosons and to the proper vertices. Our
approach is based on an application of the Lehmann-Symanzik-Zimmermann (LSZ)
reduction formula and for the special case of constant self-energies it gives
the same results as the standard approach based on the diagonalization of mass
matrices.
