A Manifestly Gauge-invariant Approach to Charged Particles 1

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-xing condition. First, we provide a thorough analysis of QED. We propose a speciic 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 phe-nomenological analyses of precision experiments at LEP. Unresolved issues include the analysis of nite width eeects 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 eeective theory, relevant for eeective eld theory analyses of the symmetry-breaking sector of the Standard Model.