Thermal Gauge Field Theories

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The real- and imaginary-time-formalisms of thermal field theory and their extension to gauge theories is reviewed. Questions of gauge (in-)dependence are discussed in detail, in particular the possible gauge dependences of the singularities of dressed propagators from which the quasiparticle spectrum is obtained. The existing results on next-to-leading order corrections to non-Abelian screening and dispersion laws of hard-thermal-loop quasiparticles are surveyed. Finally, the role of the asymptotic thermal masses in self-consistent approximations to thermodynamic potentials is described and it is shown how the problem of the apparently poor convergence of thermal perturbation theory might be overcome.
Lectures delivered at the 40th Schladming Winter School on ``Dense Matter'', 47 pages, 11 figures, LATeX2e; v2: 1 footnote and 6 references added

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