can be shown (Appendix 3) that the sume $\sigma_{ik} + E_0 \delta_{ik}$
corresponds (but coinsides in linear approximation only) to the stress tensor of
 the linear elasticity theory and turns into
pressure for isotropic media.

     Finally, the equation of the elasticity theory for an elastic
crystalline body with quasiparticle excitations in the absence of external
fields takes the form:
\begin{equation}
\frac{\partial}{\partial
t}(\rho\dot{u}_i) = - \frac{\partial\Pi_{ik}}{\partial  x_k}
 - \frac{\partial j_{0i}}{\partial t}   .$$ The last term in the right-hand side describes the force which appears when varying the quasiparticle mass current with respect to the lattice.

Let us now consider the effect of the electromagnetic field. The Maxwell’s equations are: $$\begin{aligned}
\curl{\bf E} &=& -\frac{1}{c}\,  \frac{\partial{\bf B}}{\partial t}\,
,\qquad \curl {\bf H} = \frac{4\pi}{c}{\bf j}_e + \frac{1}{c}\,
\frac{\partial{\bf D}}{\partial t} \, ,
 \\     %71
\div{\bf D} &=& 4\pi q,  \qquad \qquad \div{\bf B}  =  0,\end{aligned}$$ where ${\bf j}_e = {\bf j}'_e + q \dot {\bf u}$, $q = q_0 -e n $ is the charge density ($q_0$ being the lattice charge) and $$\quad  {\bf j}'_e = -\frac{e}{m}{\bf j}'_0 ,\quad e > 0$$ is the electron current density in the co-moving frame.

We have now to take into account the field terms in 