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

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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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Bibliographic Details
Main Author: Wetterich, Christof (Author)
Format: Article (Journal)
Language:English
Published: September 2018
In: Nuclear physics. B, Particle physics
Year: 2018, Volume: 934, Pages: 265-316
ISSN:1873-1562
DOI:10.1016/j.nuclphysb.2018.07.002
Online Access:Verlag, Volltext: http://dx.doi.org/10.1016/j.nuclphysb.2018.07.002
Verlag, Volltext: https://www.sciencedirect.com/science/article/pii/S0550321318301871
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Author Notes:C. Wetterich, Universität Heidelberg, Institut für Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg, Germany
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Summary: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 arbitrary gauge field can be mapped to an associated gauge invariant field. 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.
Item Description:Gesehen am 11.01.2019
Physical Description:Online Resource
ISSN:1873-1562
DOI:10.1016/j.nuclphysb.2018.07.002

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