At very high temperatures Yang-Mills theories can be described through perturbation theory. At the tree level the time components of the gluon fields decouple and yield a dimensionally reduced theory. The expectation value of the Polyakov loop then assumes values of the Z(N) center group. At intermediate temperatures, however, this is not true anymore. The time dependence shows up in loops. In a recent work (D.I. Diakonov, M. Oswald,  Phys. Rev.  D68, 025012 (2003)) we integrated out fast varying quantum fluctuations around background A_i and static A₄ fields. We assumed that these fields are slowly varying but that the amplitude of A₄ is arbitrary. As a result we obtained the kinetic energy terms for the Polyakov loop both for the electric and the magnetic sector of SU(2).

PACS numbers: 11.15.-q, 11.10.Wx, 11.15.Tk