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We consider the meson and baryon production in the quark-gluon plasma asapplied to the early Universe and ultrarelativistic heavy ion collisions incollider. The essential feature of our investigation is to take into account apotential barrier for quarks under meson and baryon production. We have usedthe Boltzmann equation to describe kinetic processes of quark fusion. We havederived analytic expressions for solutions of kinetic equations. This permitsto find the dependence of reaction rate on a time, temperature, mass and chargeof quarks as well as on a string tension connected with the confiningpotential. Next we have considered in detail the meson and baryon productionfor some concrete kinetic processes in collisions of ultrarelativistic heavyions. Exactly the same results will be as well true for processes in expandingUniverse

Application of Boltzmann equation to investigate kinetic processes of meson and baryon production in the quark-gluon plasma