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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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
September 2018
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| 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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| 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 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. | ||
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