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In this paper we propose a model within which the keeping of quarks inside aproton and the interaction of these quarks with quarks of another hadron can bedescribed simultaneously. The model of a three-particle bispinor field is usedfor this purpose. Such a field, in comparison with the usual one-particlefield, is considered not on Minkowski space, but on a subset of the tensorproduct of three Minkowski spaces, which is characterized by the equality oftime coordinates of three events (subset of simultaneity). Such a subset cannotbe distinguished by the Lorentz invariant method. But due to the multiparticlefield transformation law in the transition from one inertial system to anotherone, the dynamic equations for a three-particle field are consistent with theprinciple of relativity. The interaction between quarks is introduced byrequiring a local SUc(3) invariance. But in the paper a more general way toachieve this invariance than the replacement in Lagrangian of ordinaryderivatives by covariance is proposed. The applied procedure leads to atwo-index tensor of gauge field, both for Lorentz and internal indices. Theconnection of this field with the bound states of gluons - glueballs isdiscussed. It is shown that this glueball field can be represented as the sumof two terms: the classical field, which plays the role of the potential energyof quark interaction in the proton, and the field corresponding to quantumfluctuations around the classical field and describes the quark interaction inproton with other hadrons. A dynamic equation is obtained for the field thatdetermines the potential energy of quark interaction. It is shown that thisequation has solutions that correspond to the confinement of quarks.

Three-particle fields as a method of description of baryons in the scattering processes