Hello everyone:(Please forgive my poor English.)(adsbygoogle = window.adsbygoogle || []).push({});

I've been learning many-body theory for a year or so, however, I'm quite confused with different Green's functions (GF) there. One of the most things I want to get clear is about zero-temperature GF and imaginary-time GF (or Matsubara GF), both of which are time ordered.

I learned that one of the most physically interesting GF is retarded GF and all that we need to do is try to calculate it. In Mahan's book I got to know that through analytic continuation of imaginary-time GF we will get retarded GF. This is what I know.

My confusion is that if we could get retarded GF from zero-temperature GF or simply use real-time formalism if we only want to know about the ground state? Summations over Matsubara frequencies are really annoying. But I don't know how to relate the zero-temperature GF to retarded GF?

I wonder if it is possible that we begin by calculating real-time GF (time ordered) and through some transformations we get retarded GF? Or the only way to get retarded GF is to use imaginary-time GF and then analytic continuation, besides EOM and NEGF?

Looking forward to your reply! Thank you very much!

yours sincerely wiser

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# About different Green functions, I'm lost!

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