=
m\left\langle \frac{\partial\eps}{\partial {\bf p}}f\right  \rangle$$ is the quasiparticle mass current with respect to the lattice and $\rho = \rho_0
+ mn$ is the full mass density written as a sum of the lattice mass density $\rho_0$ and the quasiparticle mass density.

The quantities $\rho$ and ${\bf J}_0$ satisfy the mass continuity equation $$\dot{\rho} + \div{\bf J}_0 = 0 .$$ The full momentum ${\bf J}$ is a sum of $ {\bf J}_0$ and the field momentum ${\bf g}$: $${\bf J} = {\bf J}_0 + {\bf g}.$$ Note, that in this case [*the full momentum does not coincide with the mass flow!*]{}

Our aim is to determine momentum and energy fluxes $\Pi_{ik}$ and $\bf Q$ in such a way as to satisfy the continuity equation (51), the momentum conservation law $$\dot{J}_i + \nabla_k\Pi_{ik}   = 0,$$ and the energy conservation law $$\dot{E} + \div{\bf Q} = 0 .$$ The energy in $L$-system is given by the expression $$E = - \frac{1}{2}\rho_0\dot{\bf u}^2 + E_0(g^{\alpha\beta}) + \langle \langle
{\cal E} \varphi\rangle \rangle  + W ,$$ where $E_0(g^{\alpha\beta})$ is the strain energy in $C$-system, and $W $ is the field energy.

The time derivative of the energy (55) is then $$\begin{aligned}
\dot{E} & = 