  In this article we provide a manifestly gauge-invariant approach to charged
particles. It involves (1) Green functions of gauge-invariant operators and (2)
Feynman rules which do not depend on any kind of gauge-fixing condition. First,
we provide a thorough analysis of QED. We propose a specific set of
gauge-invariant Green functions and describe a manifestly gauge-invariant
technique to evaluate them. Furthermore we show how Green's functions and
Feynman rules of the manifestly gauge-invariant approach and of the Faddeev-
Popov ansatz are related to each other. Finally, we extend this manifestly
gauge-invariant approach to the Standard Model of electroweak interactions.
  Motivation for such an approach is abundant. A gauge-dependent framework does
obstruct not only theoretical insight but also phenomenological analyses of
precision experiments at LEP. Unresolved issues include the analysis of finite
width effects of unstable particles and of oblique corrections parametrised by,
e.g., S, T, and U. Quite another example of considerable complications caused
by a gauge-dependent framework is the matching of a full and an effective
theory, relevant for effective field theory analyses of the symmetry-breaking
sector of the Standard Model.
