Nonperturbative properties of Yang-Mills theories

Abstract

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. They also provide access to the phase diagram. 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.

Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization

“…which plays a key role in non-perturbative analyses such as the Schwinger-Dyson setup [30,31,32], remains true in presence of the Higgs field.…”

“…generalizes to the case with a fundamental Higgs field present as well. As mentioned in the introduction, this theorem is playing an important role in the study of the infrared properties of the correlation functions of non-Abelian gauge theories, see for instance [30,31,32] for applications to the study of the Schwinger-Dyson equations.…”

Reconstructing confined particles with complex singularities

“…To investigate such fundamental aspects of strong interactions, the gluon, ghost, and quark propagators in the Landau gauge have been extensively studied by both lattice and continuum methods [1][2][3]. Based on this progress, there has been recently an increasing interest in analytic structures of the gluon, ghost, and quark propagators [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Reconstructing propagators of confined particles in the presence of complex singularities

“…In the last decades, the gluon, ghost, and quark propagators in the Landau gauge have been extensively studied by both Lattice numerical simulations and semianalytical methods (for example, Dyson-Schwinger equation and Functional renormalization group), for reviews see [2][3][4], and also by models motivated by the massivelike gluon propagator of these results [5][6][7]. Based on these advances, in recent years, there has been an increasing interest in the analytic structures of the gluon, ghost, and quark propagators [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”