Non-perturbative aspects of hot QCD

I discuss some non-perturbative aspects of hot gauge theories as related to the unscreened static magnetic interactions. I first review some of the infrared divergences which cause the breakdown of the perturbation theory. Then I show that kinetic theory, as derived from quantum field theory, is a powerful tool to construct effective theories for the soft modes, which then can be treated non-perturbatively. The effective theory at the scale $gT$ follows from a collisionless kinetic equation, of the Vlasov type. The effective theory at the scale $g^2T$ is generated by a Boltzmann equation which includes the collision term for colour relaxation.