About different Green functions, I'm lost

[wiser]

Hello everyone:(Please forgive my poor English.)

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

 

[Simon Bridge]

Welcome to PF;
Looks to me like they are all part of the same overall function with different parameters to cope with specific situations. The trick is to do the physics first and the math second... let the physics lead the math.

http://en.wikipedia.org/wiki/Green's_function_(many-body_theory )