Quantum chromodynamics is studied a t finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained a t T, p =+ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated a t T, ,u + 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor a t T, ,u =+= 0 is established and the excitation spectrum of quarkgluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quarkgluon plasma the thermodynamical potential is calculated with the g3-term taken into account. The equat.ion of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases ( p = 0, T + To; T = 0, ,u + po). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta IpI -g2T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities-to found approximately the three-gluon vertex. It is shown that the solution of the equationg. obtained by iterations does not remove the infrared singularity from the temperature Green fuiictions. The nonperturbative solution of such equations is discussed.

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The grand unified theory (GUT) based on the O ( N ) and SU(N)-gauge groups after the conformally invariant gravity being included is investigated. We calculate the one-loop gravity contributions into the renormalization group equations and study their solutions. The analysis performed show that the asymptotic freedom behaviour early established for all GUT'S coupling constants is not broken by taking into account this kind of gravity. However all restrictions imposed on the GUT multiplet composition become less firmly and the physical content of the constructed models is more realistic.2) The construction of the quantum theory of gravity will possibly be a success within the super-3) Note that specific theory of gravity with higher derivatives is generated as a low energy approx-4 ) A s the canonical quantization analysis shows, five different versions of higher derivatives theory string theory developing today (see e.g. [17, 55, 561). imation in the string theory [28, 291. of gravity are possible [30].