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

• Verfasst von: Wetterich, Christof [VerfasserIn]
• Titel: Gauge-invariant fields and flow equations for Yang-Mills theories
• Verf.angabe: C. Wetterich
• Fussnoten: Gesehen am 11.01.2019
• Titel Quelle: Enthalten in: De.arxiv.org
• Jahr Quelle: 2018
• Band/Heft Quelle: (2018) Artikel-Nummer 1710.02494, 29 Seiten
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1564529444

Abstract

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.