2
$\begingroup$

this is a basic question but from what I can see it has not been asked before. I am reading Nolting's "Fundamentals of Many-Body Physics".

He speaks about the spectral density in characterising the intensity of a given spectra. He then states that the spectral density can be related to arbitrary operators and is thus closely related to retarded Green functions.

$ S_{AB}(t,t^{\prime})=\frac{1}{2\pi}\langle [A(t),B(t^{\prime})] \rangle $

From what I understand the spectral density is related to the properties of a system of particles. However the Green's function describes the propagation of a single particle. But they are equivalent. I think I am deeply misunderstanding this. Any clarification would be appreciated.

$\endgroup$
1
  • $\begingroup$ I don't have much time for a detailed answer right now, but this is a good start. Very shortly, basically a spectral function is the imaginary part of the retarded Green function. Having the spectral function is enough to reconstruct the Green function because they are related by a Hilbert transform. en.wikipedia.org/wiki/Green%27s_function_(many-body_theory) $\endgroup$ May 13, 2016 at 9:53

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.