ar X iv : h ep - p h / 03 06 17 9 v 1 1 9 Ju n 20 03 Motion of Colored Particle in Chromomagnetic Field

Dirac equation in a chromomagnetic field is solved for colored particle moving in limited space volume. Quantized energy levels and corresponding wave functions are found for a backgrounds both directed along third axes and having spherical symmetry. It was shown interrelation with the case of motion in infinite space volume. Quantum and classical mechanics of non-abelian charged particles has been studied by different authors. Problems in this theory serve to solution QCD problems and are connected with description of quark's motion inside hadrons or any other limited space volume. Since QCD has confinement property, presumably, it will be better to consider QCD problems in a finite volume as well [11]. As known, there are color background field in QCD vacuum [13 ] and so, it has sense to study the problem of motion of colored particle in color background in limited space volume. Most simple case, the constant color background could be given by two different type of vector potentials [1,2]. Problems in external color field given by abelian vector potentials are solved analoguosly to that one's in abelian theory. Second type of vector potentials are non-commuting constant vector potentials, which are not gauge equivalent to first type of one's [2]. These potentials are used to solve ground state problem of QCD [2,3] and other different problems connected with QCD vacuum [3-7] as well and sometimes give physically different results from that one's on receiving which was used first type potensials. Here we shall solve Dirac equation in finite space volume in constant chromomagnetic field given by second type vector potentials. Found solutions and spectra more suit to physical situation and by use of them it could be constructed quark's Green's function by help of exact solution method [12], which could be used in solving QCD problems.