Kohn-Sham vs Gell-Mann & Low correspondence

[thephystudent]

Both the Kohn-Sham theorem and the Gell-Mann & Low theorem provide a way to map an interacting condensed matter system on a non-interacting system, each in their own language. The Kohn-Sham approach does so for density functional theory, calculating the properties of a system from the one-electron density. On the other hand, the Gell-Mann & Low approach is used in second quantized solid-state physics where the one-electron Green function is the important object.

Despite the difference in language, is there some deeper connection between the two approaches? And what determines which one of the two languages is the one that is used?

 

[DrDu]

I think there is a decisive difference between the two approaches: In DFT, there is an extra potential introduced to make the density of the non-interacting system coincide with the density of the interacting system. There is no such potential in the Gellmann-Low approach and the densities of the interacting and non-interacting system are generically different.