Gauge-invariant fields and flow equations for Yang-Mills theories

We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant fields are constructed by consecutively adding physical flu...

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1. Verfasser: Wetterich, Christof (VerfasserIn)
Dokumenttyp: Article (Journal) Kapitel/Artikel
Sprache:Englisch
Veröffentlicht: 17 Jul 2018
In: Arxiv

Online-Zugang:Verlag, kostenfrei, Volltext: http://arxiv.org/abs/1710.02494
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Verfasserangaben:C. Wetterich

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520 |a We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant fields are constructed by consecutively adding physical fluctuations. An effective action that depends on gauge-invariant fields becomes a gauge-invariant functional of arbitrary gauge fields by associating to every gauge field the corresponding gauge-invariant field. The gauge-invariant effective action can be obtained from an implicit functional integral with a suitable "physical gauge fixing". We generalize this concept to the gauge-invariant effective average action or flowing action, which involves an infrared cutoff. It obeys a gauge-invariant functional flow equation. We demonstrate the use of this flow equation by a simple computation of the running gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory. 
650 4 |a General Relativity and Quantum Cosmology 
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