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We summarize the most important arguments why a perturbative description of finite-temperature QCD is unlikely to be possible and review various well-established approaches to deal with this problem. Then, using a recently proposed method,…
Perturbative calculations of corrections to the behavior of an ideal gas of quarks and gluons, the limit that is formally realized at infinite temperature, are obstructed by severe infrared divergences. The limits to computability that the…
Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be…
In-medium chiral symmetry breaking in confining potential models of QCD is examined. Past attempts to analyse these models have been hampered by infrared divergences that appear at non-zero temperature. We argue that previous attempts to…
Due to asymptotic freedom, QCD is guaranteed to be accessible to perturbative methods at asymptotically high temperatures. However, in 1979 Linde has pointed out the existence of an "infrared wall", beyond which an infinite number of…
I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribov's confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and…
This paper is a slightly modified version of the introductory part of a doctoral dissertation that contained also three original articles, hep-ph/0212283, hep-ph/0305183 and hep-ph/0311323. Our purpose is to review the history and present…
The QCD phase transition at finite temperature is studied with the dual Ginzburg-Landau theory, which is the QCD effective theory based on the dual Higgs mechanism by QCD-monopole condensation. At high temperature, the confinement force is…
We address the question whether we have to perform the analytic continuation to 4 space-time dimensions before or after the perturbative expansion has been made. Using the simple model of large-N scalar field theory, we show how this…
I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. By relating the Gribov confinement scenario to the center vortex picture of confinement it is shown that the Coulomb string tension is tied to the…
I review recent progress in numerical simulations of finite temperature quantum chromodynamics and discuss the status of some outstanding problems. Included is (1) a discussion of recent results determining the temperature of the ``phase…
Effective field theory methods provide a convenient approach to study static observables in field theory at finite temperature. In this talk, I will outline the construction of the effective field theory that describes effective observables…
In this work quantum electrodynamics at T > 0 is considered. For this purpose we use thermo field dynamics and the causal approach to quantum field theory according to Epstein and Glaser, the latter being a rigorous method to avoid the…
Effective-field-theory methods are used to study the high T limit of QCD. These methods unravel the contributions to the free energy of QCD at high temperature from the scales T, gT, and g^2 T. The free energy is explicitly computed to…
We evaluate thermodynamic observables such as pressure, baryon number, entropy and energy density, as well as the second and fourth order baryon number cumulants in the phase structure of QCD. The intertwined confinement and chiral dynamics…
Perturbation theory of thermodynamic potentials in QCD at $T>T_c$ is considered with the nonperturbative background vacuum taken into account. It is shown that the magnetic confinement in the QCD vacuum prevents the infrared catastrophe of…
Searching of the critical endpoint of the phase transition of Quantum Chromodynamics~(QCD) matter in experiments is of great interest. The temperature in the fireball of a collider is location dependent, however, most theoretical studies…
We study the pure-gauge QCD phase transition at finite temperatures in the dual Ginzburg-Landau theory, an effective theory of QCD based on the dual Higgs mechanism. We formulate the effective potential at various temperatures by…
We investigate the confining phase transition as function of temperature for theories with dynamical fermions in the two index symmetric and antisymmetric representation of the gauge group. By studying the properties of the center of the…
Gauge field configurations appropriate for the infrared region of QCD are proposed. Using the usual QCD action, confinement is realized as in the London theory of Meissner effect.