From two-body Green's function to one-body in perturbation theory

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SUMMARY

The discussion centers on deriving Hedin's equations used in Green's function (GW) theory. The specific equation in question is: $$G(1,3,2,3^+) = G(1,2)G(3,3^+)-\frac{\delta G(1,2)}{\delta \phi(3)}$$. The user seeks guidance on the derivation process and references a document by Luca Molinari for further reading. The need for clear derivation sources is emphasized, highlighting a gap in accessible literature on this topic.

PREREQUISITES
  • Understanding of Green's functions in quantum many-body theory
  • Familiarity with Hedin's equations in GW approximation
  • Knowledge of functional derivatives in quantum field theory
  • Experience with perturbation theory in quantum mechanics
NEXT STEPS
  • Study the derivation of Hedin's equations in the context of GW theory
  • Review the document by Luca Molinari for insights on the derivation process
  • Explore functional derivatives and their applications in quantum field theory
  • Investigate perturbation theory techniques for quantum many-body systems
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Researchers, physicists, and graduate students in theoretical physics focusing on quantum many-body theory and those specifically working with Hedin's equations in GW approximation.

forever_physicist
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Hi guys! I am trying to derive the Hedin's equations used for GW on my own, and I found this equation, but I cannot really derive it, nor find a source where they explain how this can be derived (they link to other papers that in the end don't show where this is coming from). The equation I am talking about is:
$$G(1,3,2,3^+) = G(1,2)G(3,3^+)-\frac{\delta G(1,2)}{\delta \phi(3)}$$
Can somebody tell me how this can be derived or just link me to a document with a full derivation?
Thanks!
 
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