[01] Nataliia Chudak, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [02] Maksym Deliyergiyev, Department of High Energy Nuclear Physics, Institute of Modern Physics, Lanzhou, China. [03] Kyrylo Merkotan, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [04] Oleksii Potiienko, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [05] Dmytro Ptashynskyi, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [06] Yulia Shabatura, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [07] Grygorii Sokhrannyi, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine; Department of Experimental Particle Physics, Jozef Stefan Institute, Ljubljana, Slovenia. [08] Andrii Tykhonov, Département de Physique Nucléaire et Corpusculaire, Université de Genéve, Geneva, Switzerland. [09] Yurii Volkotrub, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [10] Igor Sharph, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine. [11] Vitaliy Rusov, Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine.

The goal of the current work is to propose a model which would allow to apply the methods of quantum field theory for description of the hadron scattering as bound systems of quarks and antiquarks. From one side by applying the quantization procedure to the multi-particle fields, hadronic creation and annihilation operators have been obtained. From other side, by considering the hadron quark structure allow one describe the hadron interactions with the help of interactions of the constituent quarks and antiquarks according to the gauge principle by requiring of the local SU^c (3) symmetry. The gauge field which was obtained in this way revealed to be a multi-particle field. By analysing the dynamical equations of this multi-particle gauge field it was shown that one can impose the partialy solution of these equations. This solution allows one within same framework to describe the quark confinement as well as interactions between bound quarks by the gluon exchange. The important feature of the proposed model is that it describes the quark confinement as well as confinement of gluons.

Multi-Particle, Spinor, Pseudo-Scalar, Confinement, Asymptotic Freedom, Quakrs, Gluons, Gauge Field, Hadrons

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