  In this paper we propose a model within which the keeping of quarks inside a
proton and the interaction of these quarks with quarks of another hadron can be
described simultaneously. The model of a three-particle bispinor field is used
for this purpose. Such a field, in comparison with the usual one-particle
field, is considered not on Minkowski space, but on a subset of the tensor
product of three Minkowski spaces, which is characterized by the equality of
time coordinates of three events (subset of simultaneity). Such a subset cannot
be distinguished by the Lorentz invariant method. But due to the multiparticle
field transformation law in the transition from one inertial system to another
one, the dynamic equations for a three-particle field are consistent with the
principle of relativity. The interaction between quarks is introduced by
requiring a local SUc(3) invariance. But in the paper a more general way to
achieve this invariance than the replacement in Lagrangian of ordinary
derivatives by covariance is proposed. The applied procedure leads to a
two-index tensor of gauge field, both for Lorentz and internal indices. The
connection of this field with the bound states of gluons - glueballs is
discussed. It is shown that this glueball field can be represented as the sum
of two terms: the classical field, which plays the role of the potential energy
of quark interaction in the proton, and the field corresponding to quantum
fluctuations around the classical field and describes the quark interaction in
proton with other hadrons. A dynamic equation is obtained for the field that
determines the potential energy of quark interaction. It is shown that this
equation has solutions that correspond to the confinement of quarks.
