I found that some concepts, such as polarization and screening, met firstly in fundamental electromagnetics, are used in the context of many-body Green's functions in condensed matter physics. I am curious about the subtleties between both. Is there a deep connection between both? For completeness, let me first explain the two physical picture in detail.

1. Viewpoint from the fundamental electromagnetics

[![enter image description here](https://i.stack.imgur.com/qZu6Y.png)](https://i.stack.imgur.com/qZu6Y.png)

As shown above, if we applied an external electric field $\vec{E}\_0$ to a homogeneous (constant dielectric function) and infinite dielectric materials (ignoring boundary conditions), then charges will move in response to $\vec{E}\_0$. Along with charge moves, the dipole moment will be formed. **Correspondingly, the dipole moment per unit volume is defined as dielectric polarization $\vec{P}$.** The average charge density is still zero, but the induced (depolarizing) electric field $\vec{E}\_1$ will weaken the applied $\vec{E}\_0$. **The local electric field will be introduced:
$$\vec{E}\_{local}=\vec{E}\_0+\vec{E}\_1 ,$$
which plays the role of screening.** **If we consider only linear effects, one can found further the following relation:
$$\vec{P}=\epsilon\_0\chi\_e\vec{E}.$$**
The dielectric displacement is defined as:
 $$\vec{D}=\epsilon\_0\vec{D}+\vec{P}$$
then we find
$$\vec{D}=\epsilon\_0\epsilon\vec{E}$$
with $\epsilon=1+\chi\_e$.

2. Viewpoint from many-body Green's function:

[![enter image description here](https://i.stack.imgur.com/wqVAE.png)](https://i.stack.imgur.com/wqVAE.png)

The physical picture from the viewpoint of many-body Green's function is explained in the above figure. **One can see the concepts of polarization and screening again.** In particular, the polarization will be translated to polarization response function and screening will be represented by the dielectric function.

I cannot believe there is a coincidence here. So the many-body Green's function borrows some concepts from fundamental electromagnetics? Or two viewpoints for the same physics just from macroscopic and microscopic view?