Finite Temperature Effective Theories

High-temperature and dense matter of elementary particles appears in several areas of physics. The rst and most familiar example is the Universe at the early stages of its expansion. The Big Bang theory (for reviews see, e.g. ) states that the Universe was hot and dense in the past, with a temperature ranging from a few eV up to the Planck scale MPl 10 GeV. Another place, where matter exists in extreme conditions of high densities, can be created in the laboratory. Namely, in heavy-ion collisions extended dense reballs of nuclear matter are created, with the energy density exceeding the QCD scale 10 (200MeV ). From a practical point of view, there is quite a wide area of applications of nite-temperature eld theory to cosmology and laboratory experiments. The high-temperature phase transitions, typical for grand uni ed theories (GUTs), may be important for cosmological in ation and primordial density uctuations. Topological defects (such as monopoles, strings, domain walls) can naturally arise at the phase transitions and in uence the properties of the Universe we observe today. The rst-order electroweak (EW) phase transition is a crucial element for electroweak baryogenesis; it may also play a role in the formation of the magnetic elds observed in the Universe. The QCD phase transition and properties of the quark-gluon plasma are essential for the understanding of the physics of heavy-ion collisions. The QCD phase transition in cosmology may in uence the spectrum of the density uctuations relevant to structure formation. In most cosmological applications, the deviations from thermal equilibrium play a most important role. For example, the concentration of primordial monopoles depends a lot on the dynamics of the grand uni ed phase transition; the baryonic asymmetry, produced in GUTs or in the EW theory, depends on the rate of the Universe expansion or other time-dependent phenomena. The signatures of the heavy-ion collisions are greatly in uenced by the non-equilibrium dynamics. The study of non-equilibrium properties of the