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Huber, Markus Q.

Nonperturbative properties of Yang-Mills theories. (English) Zbl 1472.81166

Phys. Rep. 879, 1-92 (2020).
Summary: Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations or properties of its phase diagram with functional methods. Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson-Schwinger equations. Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang-Mills theories.

Cited in 5 Documents

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81V22 Unified quantum theories
81V05 Strong interaction, including quantum chromodynamics
81V35 Nuclear physics
81V73 Bosonic systems in quantum theory

Keywords:

Yang-Mills theory; quantum chromodynamics; functional equations; Dyson-Schwinger equations; \(n\) PI effective actions; correlation functions; propagators; vertices; Landau gauge; Coulomb gauge; linear covariant gauges; maximally abelian gauge; confinement

Software:

FeynCalc; DoFun; Mathematica; FeynHelpers; JaxoDraw; FormTracer; CrasyDSE; TRACER; FORM; HEPMath
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