The High-Temperature Phase of Yang-Mills Theory in Landau Gauge
The finite and high temperature equilibrium properties of Yang-Mills theory in Landau gauge are studied. Special attention is paid to the fate of confinement and the infrared properties at high temperatures. The method implemented are the equations of motion, the Dyson-Schwinger equations. A specifi...
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| Format: | Others |
| Language: | English en |
| Published: |
2004
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| Online Access: | https://tuprints.ulb.tu-darmstadt.de/504/1/thesis.pdf Maas, Axel Torsten <http://tuprints.ulb.tu-darmstadt.de/view/person/Maas=3AAxel_Torsten=3A=3A.html> (2004): The High-Temperature Phase of Yang-Mills Theory in Landau Gauge.Darmstadt, Technische Universität, [Online-Edition: http://elib.tu-darmstadt.de/diss/000504 <http://elib.tu-darmstadt.de/diss/000504> <official_url>],[Ph.D. Thesis] |
| Summary: | The finite and high temperature equilibrium properties of Yang-Mills theory in Landau gauge are studied. Special attention is paid to the fate of confinement and the infrared properties at high temperatures. The method implemented are the equations of motion, the Dyson-Schwinger equations. A specific approximation scheme is introduced, which was previously applied successfully to the vacuum. In a first step, the infinite temperature limit is taken. The theory reduces to a 3-dimensional Yang-Mills theory coupled to a massive adjoint Higgs field. The equations for the propagators of the Higgs, the gluon, and the Faddeev-Popov ghost are obtained. They are solved in the infrared analytically and at least in the Yang-Mills sector confinement is found. Therefore the high-temperature phase of a 4-dimensional Yang-Mills theory is non-trivial and strongly interacting. Solutions for all propagators are obtained numerically at all momenta. Thereby also the propagators of a pure 3-dimensional Yang-Mills theory are determined. Systematic studies find only quantitative effects of the errors, which are induced by the approximations. Good agreement to lattice calculations is found. Finite temperatures down to the regime of the phase transition are investigated. It is found that the infrared properties are only quantitatively affected, and confinement of gluons transverse to the heat bath is established. The hard modes are nearly inert even at temperatures of the order of the phase transition temperature. Therefore the infinite temperature limit is a good approximation already at temperatures a few times the critical temperature, in agreement with lattice calculations. Finally quantities derived from the propagators are studied. The Schwinger functions are calculated. It is found that also the gluons longitudinal with respect to the heat bath are strongly influenced by higher order or even genuine non-perturbative effects, even in the infinite temperature limit. The analytic structure of the gluon propagator is investigated, and it is found that at least gluons transverse to the heat bath comply with the Kugo-Ojima and Zwanziger-Gribov confinement scenarios. Investigating the thermodynamic potential, an approximate Stefan-Boltzmann-like behavior is found. The thermodynamic potential, but not necessarily the pressure, is dominated by the hard modes. By comparison with calculations below the phase transition and lattice calculations it is conjectured that Yang-Mills theory likely undergoes a first order phase transition, which changes a strongly interacting system into another. The phases differ mainly by the properties of the chromoelectric sector. |
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