gauge group. The equations of motion for the Yang-Mills field are

\_\^=-\[3\] where the covariant derivative is

\_=\_-ig\[4\] $\mathbf{Q}$ is a projection operator

=2\_a\_a\_a=-1n \[4.01\] Eq. (\[3\]) implies the Bianchi identity

=0 \[5\]

We also have the energy-momentum tensor

T\^\_[YM]{}=\^\_[YM]{} \[6\] where

\^\_[YM]{}=\^\_\^-14g\^\^\_ \[7\] is traceless in world indices. Using the identity $\mathbf{D}_{\left(\mu\right.}\mathbf{F}_{\left.\nu\lambda\right)}=0$ (where brackets mean symmetrization) we get

{\_\^\_[YM]{}+\_\^}=0 \[8\]

Kinetic theory {#kin}
--------------

In principle the scalar matter should be described by quantum field theory. The reduction of the nonequilibrium quantum field description to kinetic theory is fairly established by now, see e.g. [@libro] and references therein.

The kinetic equation which governs the evolution of the one-particle distribution matrix $\mathbf{f}$ reads [@HeinzPRL; @Heinz] (see also [@libro; @elze; @BlaizotIancu; @winter; @Litim]) p\^=(p\^0)\_[col]{} \[9\] where \_ = \_ - ig \[\_,\] with $\mathbf{A}_\mu$ expressed in the fundamental representation. $\mathbf{f}\left(X,p\right)$ is an $N\times N$ matrix ($N=3$ for quarks) and obeys $\mathbf{f}^{\dagger}\left(X,p\right)=\mathbf{f}\left(X,p\right)$.

The collision kernel on the right hand side encodes the interaction among the hard excitations of the matter field, and is, in general, a complicated functional of the self-energy [@libro]. However, to carry out our developments we really do not need to consider it in much detail, and we anticipate 