Using Heisenberg equations for the operators $\underline{D}_\lambda
$ and $\underline{A}_\lambda $ , that is $$\begin{aligned}
\label{c26}
&&\underline{\dot{A}}_\lambda (
\vec{k},t)=\frac{\imath}{\hbar}\left[ H \ , \underline{A}_\lambda (
\vec{k},t)\right]= -\ \frac{\underline{D}_\lambda (
\vec{k},t)-\vec{e}_{\lambda\vec{k}}\ \cdot\ \underline{\vec{P}}(\vec{k},t)}{\varepsilon_0}\nonumber\\
&&\underline{\dot{D}}_\lambda (
\vec{k},t)=\frac{\imath}{\hbar}\left[ H \ , \underline{D}_\lambda (
\vec{k},t)\right]=\frac{|\vec{k}|^2}{\mu_0}\underline{A}_\lambda (
\vec{k},t) - \vec{e}_{\lambda\vec{k}}\ \cdot\  \left(
\imath\vec{k}\times
\underline{\vec{M}}(\vec{k},t)\right)\nonumber\\
&&\end{aligned}$$ Maxwell equations can be obtained as is expected. Multiplying both sides of Eqs (\[c26\]) in the polarization unit vector $\vec{e}_{\lambda\vec{k}}$ and then summation on polarization index $ \lambda=1,2 $ and using (\[c18\])clearly give us $$\label{c27}
\underline{\vec{D}}(\vec{k},t)=\varepsilon_0
\underline{\vec{E}}(\vec{k},t)+\underline{\vec{P}}(\vec{k},t)$$ $$\label{c27.1}
\underline{\dot{\vec{D}}}(\vec{k},t)=\imath\vec{k}\times\underline{\vec{H}}$$ where  $\displaystyle
\underline{D}=\sum_{\lambda=1}^2\underline{\dot{D}}_\lambda
\vec{e}_{\lambda\vec{k}}$  plays the role of the displacement field, $\displaystyle\underline{\vec{E}}=-\underline{\dot{\vec{A}}}-\imath\vec{k}\underline{\varphi}=
-\underline{\dot{\vec{A}}}-\frac{\hat{k}(\hat{k}\cdot\underline{\vec{P}})}{
\varepsilon_0}$ is the total electric field and $\displaystyle\underline{\vec{H}}(\vec{k},t)=\frac{\imath\vec{k}\times
\underline{\vec{A}}}{\mu_0}-\underline{\vec{M}}$ is the magnetic induction field.\

 The constitutive equations of the medium
=========================================

It is well known that the constitutive equations of a responding medium are the consequences of the interaction of the medium with electromagnetic field. Any quantization method such as this theory, in which the medium enter directly in the process of quantization and the interaction of the medium with the vacuum field is explicitly given, must be able to give the constitutive equations of the medium using the Heisenberg equations of the total system. Also the susceptibility tensors 