On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions

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Springer Science & Business Media, Feb 14, 2012 - Mathematics - 137 pages
Quarks 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
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