9
$\begingroup$

The Random Phase Approximation (RPA) is a technical method used in field theory to account for interactions when calculating correlation functions. It consists of only keeping a certain class of diagrams when doing a perturbative calculation of a certain function, such as a susceptibility or dielectric function.

Is there a simple mathematical justification to this method, other than "it is simple and it fits experimental data", which is already a good justification? Why don't we include the vertex corrections and other self-energy terms?

$\endgroup$
  • $\begingroup$ See Altland-Simons page 216. Basically, the RPA Feynman diagrams have the largest contribution in the limit of high electron density. $\endgroup$ – leongz May 24 '17 at 9:02
  • $\begingroup$ Thanks, exactly what I was looking for ! If you want to elaborate your comment into an answer I will accept it. $\endgroup$ – Dimitri May 24 '17 at 10:18
2
$\begingroup$

RPA is the first order approximation in $1/N$ (which is often called the Large-$N$ expansion), where $N$ is the number of fermions in the system. In the system with spin up and spin down, then $N=2$. Therefore, RPA is exact in the hypothetical system with $N\rightarrow \infty$.

$\endgroup$
  • $\begingroup$ Thanks. In usual theories $N$ is no larger than $2$ or $3$, so is the limit $N \rightarrow \infty$ really relevant ? $\endgroup$ – Dimitri Apr 3 '17 at 13:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.