@misc{Bazak_Sylwia_Anna_Stability,
 author={Bazak, Sylwia Anna},
 howpublished={online},
 school={Uniwersytet Jana Kochanowskiego w Kielcach},
 language={eng},
 abstract={In the Color Glass Condensate formalism, the system of gluons called glasma, formed in an earliest phase of nuclear collision at the highest available energies, is described in terms of classical chromodynamic fields. This dissertation considers the stability of the initial configuration of these classical fields. Our work was motivated by computer simulations suggesting the existence of instabilities in the early phase of relativistic heavy-ion collisions, and the goal of our research was to understand the nature of these instabilities. To achieve this, we performed a systematic linear stability analysis of the initial glasma configuration by solving the linearized Yang- Mills equations. Chromoelectric and chromomagnetic fields, which can be treated approximately as constant and uniform were considered. In the first part of the thesis, the focus is on the comparison of the solutions for the same background fields, however generated by the potentials in two ways: as in electrodynamics, where constant and homogeneous electric and magnetic fields correspond to potentials linearly dependent on coordinates, and in the way characteristic of non-Abelian theories, where constant and uniform fields also appear due to a non-zero commutator of constant potentials. The linearized Yang-Mills equations were fully algebraized by performing a Fourier transformation, and the use of a suitable gauge condition - background gauge, made it possible to find exact general solutions and compare different cases. In the subsequent part of the work, the gauge independent energy-momentum tensor of the considered system was found. It allowed to determine, in particular, the time evolution of the energy density. Moreover the stability of the configuration of simultaneous chromoelectric and chromomagnetic fields was studied. The third part of the work deals with the stability analysis, that was performed by considering the conditions to be as similar as possible to the ones of real heavy-ion collisions. This was done using both Milne coordinates, which are natural for the description of glasma, and the Fock-Schwinger gauge condition. The limitations of space homogeneity and the fact that the background fields evolve in time were also discussed. Unstable modes were found in the system under consideration, but their occurrence requires special conditions. The analysis also shows that the instabilities found in the lattice simulations by Romatschke and Venugopalan are not those of the initial glasma, as it was claimed by some authors.},
 title={Stability of classical non-Abelian field configurations},
 type={rozprawa doktorska},
}