A transport model with color confinement

First the mostly important properties of QCD are dealt with. It is made plausible, how the QCD vacuum generates a screening of color charges and is by this responsible for the quark confinement in color singlets. in the following the behaviour of classical color charges and color fields is studied and it is concluded that by this approximation, the neglection of quantum-mechanical fluctuation, the quark confinement cannot be explained, because the mean-field approximation leads to a screening of the color charges. Motivated by this result the Friedberg-Lee soliton model is presented, in which the the color confinement and all further nonperturbative QCD effects are phenomenologically modelled by means of a scalar field. Thereafter a derivation of the transport equations for quarks in the framework of the Wigner-function is presented. An extension of the equation to the Friedberg-Lee model is explained. As results the ground-state properties of the model are studied. Mesonic and baryonic ground-state solutions (soliton solutions) of the equations are constructed, whereby the constituents are both light quarks and heavy quarks. Furthermore the color coupling constant of QCD is fixed by means of the string tension by dynamical separation of the quarks of the meson. The flux tubes formed dynamically in this way are applied, in order to study the interaction of two strings and to calculate a string-string potential. Excited states of the meson (isovectorial modes) are presented as well as the influence of the color confinement on the quark motion. Finally the dynamical formation and the break-up of a string by the production of light and heavy quark pairs is described