The constant background bag model of the hadron

We have constructed the bag model having a central constant color field. The motion of the quark is studied in this bag and the Dirac equation is solved for it. The energy spectrum found has a branching due to the interaction of the quarks with the color background. It is pointed out that this model can be applied for taking into account, in the mass spectrum of hadrons, the coupling of the constituent quarks with the gluon condensation as the interaction with the color background.