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Sometimes the dielectric function is defined as the connection between the total electric field in a material and the external field,

[tex]

\mathbf{E}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) \mathbf{E}_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'},

[/tex]

and sometimes as the connection between the total effective potential and the externally applied potential,

[tex]

V_{\text{tot}}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) V_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'}.

[/tex]

I don't see how these two definitions are equivalent.

See, e.g. "etsf.grenoble.cnrs.fr/dp/tutorial/dptutorial.pdf" [Broken] and "cms.mpi.univie.ac.at/mmars/ThesisJudithHarlChapter2.pdf" [Broken].

Could somebody comment on that?

[tex]

\mathbf{E}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) \mathbf{E}_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'},

[/tex]

and sometimes as the connection between the total effective potential and the externally applied potential,

[tex]

V_{\text{tot}}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) V_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'}.

[/tex]

I don't see how these two definitions are equivalent.

See, e.g. "etsf.grenoble.cnrs.fr/dp/tutorial/dptutorial.pdf" [Broken] and "cms.mpi.univie.ac.at/mmars/ThesisJudithHarlChapter2.pdf" [Broken].

Could somebody comment on that?

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