## On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green FunctionsQuarks are the main constituents of protons and neutrons and hence are important building blocks of all the matter that surrounds us. However, quarks have the intriguing property that they never appear as isolated single particles but only in bound states. This phenomenon is called confinement and has been a central research topic of elementary particle physics for the last few decades. In order to find the mechanism that forbids the existence of free quarks many approaches and ideas are being followed, but by now it has become clear that they are not mutually exclusive but illuminate the problem from different perspectives. Two such confinement scenarios are investigated in this thesis: Firstly, the importance of Abelian field components for the low-energy regime is corroborated, thus supporting the dual superconductor picture of confinement and secondly, the influence of the Gribov horizon on non-perturbative solutions is studied. |

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### Contents

1 Introduction | 1 |

2 YangMills Theory and its Infrared Behavior | 7 |

3 Functional Equations | 25 |

4 Scaling Solutions | 36 |

5 The Infrared Regime of the Maximally Abelian Gauge | 59 |

6 DysonSchwinger Equations in the Gribov Region | 81 |

7 Conclusions | 107 |

Appendix A Details on the Formulae for the Scaling Analysis | 109 |

Appendix B Grassmann Fields | 116 |

Appendix C Feynman Rules of the Maximally Abelian Gauge | 121 |

Appendix D Calculation of the Sunset Diagram | 123 |

Appendix E Deriving DysonSchwinger Equationswith DoDSE | 125 |

Curriculum Vitae | 136 |

### Other editions - View all

On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions Markus Q. Huber No preview available - 2014 |

### Common terms and phrases

Alkofer analysis arXiv:hep Behavior of Yang-Mills C.S. Fischer calculations cancelations color confinement scenarios correlation functions corresponding Cucchieri denoted derived determine diagonal gluon divergent DoDSE dominance dressing functions DSEs Dyson-Schwinger Equations Faddeev-Popov ghosts Faddeev-Popov operator fermionic field configurations ﬁelds four-point functions FRGEs functional equations gauge field gauge fixing Gauge Fixing Aspects ghost propagator ghost-gluon vertex given gluon field gluon propagator Grassmann fields Green functions Gribov horizon Gribov region Gribov-Zwanziger action hep-lat hep-th inequalities Infrared Infrared Behavior interactions IREs J.M. Pawlowski Kugo Lagrangian Landau gauge leading diagrams Lett loop Lorentz M.A.L. Capri M.Q. Huber Maas maximally Abelian gauge mixed propagators momentum n-point functions non-perturbative Nucl obtained Ojima parameter path integral Phys possible power laws quarks S.P. Sorella scaling relation scaling solution Schwenzer Sect Smekal SU(N tensor thesis three-point functions two-point DSEs V.E.R. Lemes vanish Yang-Mills theory zero Zwanziger