One of the most interesting predictions of QCD is a phase transition at some critical temperature to a new phase of strongly interacting fields: the quark-gluon plasma. The quark-gluon plasma is a state of strongly interacting matter (with the quarks and gluons) where they are not longer confined to color neutral entities of hadronic size. The quark-gluon plasma is a state of matter at temperatures above the phase transition temperature and this state is characterized by a weak coupling constant . At the temperatures below the phase transition temperature we have strong coupling constant and we should use nonperturbative technique to describe quantum fields in this region. The various methods can be employed to describe the thermodynamics of the high temperature quark-gluon plasma (for review, see [1-4] and references therein).

Currently one of the biggest problems (in our opinion it is a challenge) in quantum field theory is the problem of a nonperturbative quantization. The problem is that for strongly interacting fields we cannot apply quantization recipes designed for weakly interacting fields. From a mathematical point of view it means that in this case the Feynman diagram technique cannot be applied. From a physical point of view it means that quantum strongly interacting fields cannot be presented as a cloud of interacting quanta. Rather such field can be compared with a turbulent fluid flow. In this flow there is a statistically fluctuating field of velocities. The velocities in the two sufficiently close points are correlated with each other. It was exactly what we have for strongly interacting quantum fields: the value of the quantum field in the two close enough spacelike points are correlated with each other. It means that the correlation function of these fields (2-point Green's function) in two sufficiently close spacelike points is nonzero. It has been noted by W. Heisenberg [5]. Evidently only one difference between quantum fields and turbulent fluid is that in the quantum case corresponding quantum states will be quantized. As it should be in quantum theory.

The quantum states describing the distribution of strongly interacting quantum fields will be called as quantum correlated states of strongly interacting fields. Briefly, quantum correlated states. For simplicity, in the future we will consider only the SU(3) non-Abelian gauge field without quarks.

The main goal of our research is a qualitative explanation of the phase transition for gluon field as a transition from the statistics of a gas of nonperturbative interacting gluons to the statistics nonperturbative correlated quantum states of strongly interacting SU(3) gauge field.

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