Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories.
TL;DR: A controlled extrapolation of lattice data to infinite volume is performed, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions.
Abstract: We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.
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TL;DR: The Gribov-Zwanziger framework as mentioned in this paper allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gibov region.
Abstract: Recent lattice data have reported an infrared suppressed, positivity violating gluon propagator which is nonvanishing at zero momentum and a ghost propagator which is no longer enhanced. This paper discusses how to obtain analytical results which are in qualitative agreement with these lattice data within the Gribov-Zwanziger framework. This framework allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gribov region. We elaborate to great extent on a previous short paper by presenting additional results, also confirmed by the numerical simulations. A detailed discussion on the soft breaking of the Becchi-Rouet-Stora-Tyutin symmetry arising in the Gribov-Zwanziger approach is provided.
496 citations
TL;DR: In this article, the authors present recent results for the Landau-gauge gluon and ghost propagators in SU (3 ) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L = 64 to L = 96 at β = 5.70, thus reaching “deep infrared” momenta down to 75 MeV.
439 citations
01 Jan 2005
378 citations
TL;DR: In this paper, the properties of ghost and gluon propagators in the deep infrared momentum region of Landau gauge Yang-Mills theory were discussed. And it was shown that it is only a matter of infrared boundary conditions whether infrared scaling or decoupling occurs.
318 citations
TL;DR: In this paper, the properties of ghost and gluon propagators in the deep infrared momentum region of Landau gauge Yang-Mills theory were discussed. And it was shown that it is only a matter of infrared boundary conditions whether infrared scaling or decoupling occurs.
Abstract: We discuss the properties of ghost and gluon propagators in the deep infrared momentum region of Landau gauge Yang-Mills theory. Within the framework of Dyson-Schwinger equations and the functional renormalization group we demonstrate that it is only a matter of infrared boundary conditions whether infrared scaling or decoupling occurs. We argue that the second possibility is at odds with global BRST symmetry in the confining phase. For this purpose we improve upon existing truncation schemes in particular with respect to transversality and renormalization.
282 citations
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19 Sep 2005TL;DR: A review of Monte Carlo methods of computer simulation can be found in this article, where a brief review of other methods of simulation can also be found, as well as a brief introduction to Monte Carlo studies of biological molecules.
Abstract: Preface 1. Introduction 2. Some necessary background 3. Simple sampling Monte Carlo methods 4. Importance sampling Monte Carlo methods 5. More on importance sampling Monte Carlo methods of lattice systems 6. Off-lattice models 7. Reweighting methods 8. Quantum Monte Carlo methods 9. Monte Carlo renormalization group methods 10. Non-equilibrium and irreversible processes 11. Lattice gauge models: a brief introduction 12. A brief review of other methods of computer simulation 13. Monte Carlo simulations at the periphery of physics and beyond 14. Monte Carlo studies of biological molecules 15. Outlook Appendix Index.
2,055 citations
01 Jan 2005
378 citations
"Constraints on the infrared behavio..." refers background in this paper
...This property is known as self-averaging [29] and is the behavior expected for extensive quantities in pure phases, away from phase boundaries....
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