of the medium which are a measure for the polarizability of the medium should be specified in terms of the parameters describing the interaction of the medium with electromagnetic field. In this section, we find the constitutive equations of the medium using the Heisenberg equations of the dynamical fields modeling the medium. As we do this, the electric and magnetic susceptibility tensors of the medium are naturally found in terms of the coupling tensors $f$ and $g$. In the Heisenberg picture, using the commutation relations (\[c24\]) and the total Hamiltonian (\[c25\]), the equations of motion for the canonical variables $ \underline{X}_{\omega\lambda}\  ,\
\underline{Q}_{\omega\lambda} \hspace{00.50 cm} \lambda=1,2,3 $ for each wave vector in the half space $ k_z\geq 0 $ follow as $$\begin{aligned}
\label{c28}
\underline{\dot{X}}_{\omega\lambda}(\vec{k},t)
&=&\frac{\imath}{\hbar}[ H ,
\underline{X}_{\omega\lambda}(\vec{k},t)]=\underline{Q}_{\omega\lambda}(\vec{k},t)\nonumber\\
\underline{\dot{Q}}_{\omega\lambda}(\vec{k},t)&=&[ H ,
\underline{Q}_{\omega\lambda}(\vec{k},t)]= -
\omega^2\underline{X}_{\omega\lambda}(\vec{k},t) + \int d^3q
\underline{f}^*_{ij}( \omega , \vec{q} , \vec{k})
\underline{E}^i(\vec{q},t)
 e^{j}_{\lambda\vec{k}}\nonumber\\
 &&\end{aligned}$$ where $\displaystyle\underline{\vec{E}}(\vec{q},t)=-\underline{\dot{\vec{A}}}(\vec{q},t)-\frac{\hat{q}\left(\hat{q}\cdot\underline{\vec{P}}(\vec{q},t)\right)}{\varepsilon_0}$ is the Fourier transform of the total electric field. Multiplying both sides of Eqs. (\[c28\]) in the mutually orthogonal unit vectors $ \vec{e}_{\lambda\vec{k}}$ and then summation on $\lambda=1,2 ,3$ and using the completeness relations $\displaystyle
\sum_{\lambda=1}^3
e^{i}_{\lambda\vec{k}}e^{j}_{\lambda\vec{k}}=\delta_{ij}$ we find $$\label{c29}
\underline{\ddot{\vec{X}}}(\vec{k},t)+\omega^2
\underline{\vec{X}}(\vec{k},t)= \int d^3q\ \underline{f}^\dag
(\omega , \vec{q}, \vec{k})\ \cdot\ \underline{\vec{E}}(\vec{q},t)$$ This 