\frac{\p \eps}{\p {\bf p}}$ is the average momentum (the
mass flow) in  C-system. \par
Equations (33)-(36) replace the Galilean transformations, which are not valid
for quasiparticles because of the priviged of the crystal lattice frame.
\par
We are able now to write the Boltzmann equation:
\begin{equation}
\frac{\p f}{\p t} + \frac {\p f}{\p {\bf r}} \frac {\p H}{\p {\bf p}}
-\frac{\p f}{\p {\bf p}}
\left(\frac{\p H}{\p {\bf r}} - {\bf F}\right) = \hat{ I} f
\ee            %37
where $\hat{I}$ is the collision operator. Note, that this  equation
becomes well
defined for quasiparticles only after obtaining the Hamiltonian
and the Hamilton equations.
\par
It has been shown in \cite{AP} that this equation is compatible with the
requirement of periodicity. This  can be seen also from its form if
$
f(\mbox{\boldmath $\kappa$}, {\bf r}, t)$ is taken as a function
of the invariant quasimomentum
{\boldmath $\kappa$} and the quantities
$\bf p$ and $H$ are substituted from (33) and (34). This yields:
\begin{equation}
\frac{\d f}{\d t} + {\bf a}_{\alpha}\frac{\partial\eps}{\partial
\kappa_{\alpha}}\left(\frac{\partial f}{\partial {\bf
r}}\right)_{\mbox {\boldmath $\kappa$}} -
{\bf a}_{\alpha}\frac{\partial f}{\partial
\kappa_{\alpha}}\left\{m\frac{\d \dot{\bf u}}{\d t} +
\left(\frac{\partial\eps}{\partial {\bf r}}\right)_{\mbox {\boldmath $\kappa$}}
  - m
\frac{\partial\eps}{\partial  \kappa_{\beta}}{\bf  a}_{\beta}\times
\curl \dot{\bf u} - {\bf F}\right\} = \hat{I}f$$ where 