We discuss the concept of gauge-invariant fields for non-abelian gaugetheories. Infinitesimal fluctuations around a given gauge field can be splitinto physical and gauge fluctuations. Starting from some reference field thegauge-invariant fields are constructed by consecutively adding physicalfluctuations. An effective action that depends on gauge-invariant fieldsbecomes a gauge-invariant functional of arbitrary gauge fields by associatingto every gauge field the corresponding gauge-invariant field. Thegauge-invariant effective action can be obtained from an implicit functionalintegral with a suitable "physical gauge fixing". We generalize this concept tothe gauge-invariant effective average action or flowing action, which involvesan infrared cutoff. It obeys a gauge-invariant functional flow equation. Wedemonstrate the use of this flow equation by a simple computation of therunning gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory.
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