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

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The discussion focuses on deriving Hedin's equations for the GW approximation, specifically the equation involving the two-body Green's function. The user expresses difficulty in finding a source that clearly explains the derivation of the equation G(1,3,2,3^+) = G(1,2)G(3,3^+) - δG(1,2)/δφ(3). A suggested resource for a complete derivation is provided, linking to a relevant publication on ResearchGate. The conversation highlights the challenges in accessing clear and direct derivations in academic literature. Overall, the thread emphasizes the need for accessible explanations in complex theoretical frameworks.
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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