A Manifestly Gauge-Invariant Approach to Charged Particles

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.