Phase transition for gluon field: a qualitative analysis

Abstract

The phase transition for SU(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 $ \approx 1.5 \cdot 10^3$ Mev then it is found that the corresponding value of coupling constant lies in the nonperturbative region.