Scientific Journal of KubSAU

The phase transition for US(3) gauge field (without quarks) is considered. It is shown that the phase transition is due to the fact that at high temperatures the partition function should be calculated as for a gas of gluons, whereas at low temperatures as the sum over energy levels of correlated quantum states of SU(3) gauge field. A correlated quantum state for strongly interacting fields is defined as a nonperturbative quantum state of strongly interacting fields. The energy spectrum of these quantum states are discrete one. A lower bound of the phase transition temperature by comparing of the average energy for the perturbative and nonperturbative regimes is estimated (for glueball being in thermal equilibrium with the thermostat). It is shown that this quantity is associated with a mass gap. In a scalar model of glueball its energy is calculated. It is shown that this energy is the mass gap. If we set the glueball mass ~ 1.5•10³MeV then it is found that the corresponding value of coupling constant lies in the nonperturbative region

In a scalar approximation the distribution of a gluon condensate in a glueball is calculated. In this approximation the SU(3) gauge fields are separated on two parts: (1) is the subgroup, (2) is the coset . Using an approximate nonperturbative quantization technique two scalar fields are applied for the description of the SU(2) and coset degrees of freedom. In this approach 2-point Green's functions are a bilinear combination of scalar fields and 4-point Green's functions are the product of 2-points Green's functions