  Gauge-invariant perturbation theory is an extension of ordinary perturbation
theory which describes strictly gauge-invariant states in theories with a
Brout-Englert-Higgs effect. Such gauge-invariant states are composite operators
which have necessarily only global quantum numbers. As a consequence, flavor is
exchanged for custodial quantum numbers in the standard model, recreating the
fermion spectrum in the process. Here, we study the implications of such a
description, possibly also for the generation structure of the standard model.
In particular, this implies that scattering processes are essentially
bound-state-bound-state interactions, and require a suitable description. We
analyze the implications for the pair-production process $e^+e^-\to{\bar f}f$
at a linear collider to leading order. We show how ordinary perturbation theory
is recovered as the leading contribution. Developing a suitable PDF-type
language, we also assess the impact of sub-leading contributions. We find that
only for very heavy fermions in the final state, especially top quarks, sizable
corrections could emerge. This gives an interesting, possibly experimentally
testable, scenario for the formal field theory underlying the electroweak
sector of the standard model.
