\frac{\partial}{\partial{\bf p}}$$ $$\begin{aligned}
\langle f\ldots  \rangle
& \equiv &
\int\frac{d^3p}{(2\pi\hbar)^3}f({\bf p},
{\bf r},t)\ldots
 = \frac{1}{\sqrt g}  \int\frac{d^3
\kappa}{(2\pi\hbar)^3}f({\bf p},{\bf r},t)\ldots   \nonumber \\
&  =  &  \int \frac{d^3   \kappa}{(2\pi\hbar)^3}
\varphi(\mbox {\boldmath $\kappa$}, {\bf r}, t) \ldots
\equiv
\langle \langle \varphi\ldots
\rangle \rangle \, ,\end{aligned}$$ $$\int  d^3 r\ldots  = \int d^3 N^{\alpha} g^{1/2}  \ldots$$

 Conservation Laws and Dynamics Equations
=========================================

In order to avoid cumbersome expressions we shall make our consideration in three steps. First we write the conservation laws and consider the problem in a general form without taking into account the explicit form of the Maxwell’s equations and electromagnetic forces. Then we consider Maxwell’s equations and constitute relations for moving media and finally we combine the results and obtain the full selfconsistent set of equations.

We start with the conservation laws.

The continuity equation for quasiparticles is $$m\dot{n} + \div {\bf j}_0 = 0$$ where $$n =\langle\langle\varphi\rangle \rangle = \langle f\rangle ,
  \quad {\bf j}_0 =
m\left\langle \frac{\partial H}{\partial {\bf p}}f\right  \rangle =
m\left\langle \frac{\partial\eps}{\partial {\bf p}}f\right  \rangle
+ m n {\bf \dot u}.$$

This equation follows directly from the kinetic equation [@Push].

The total mass current is $${\bf J}_0   = \rho\dot{\bf u} + {\bf j}'_0 ,$$ where $${\bf j}'_0 