I have done a problem with a spin two electron spin system. I have found the Greens function propagator for spin up->spin up, which I have written in a form where the occupancy of spin up electrons is incorparated (attached) and from there I can get the spectral function, which will then be something like (omitting some factors): A=(1-N_up)δ(ω-E-U) + N_upδ(ω-E) But I am not sure how to interpret it. I know that for free electrons the spectral function A(k,ω) is something about how we can add an electron with momentum k to the system only by adding an electron with energy ω=E. But this can't be translated directly to how we can add an electron with spin up to the system since that would be impossible for 2 of the possible 4 configurations due to pauli exclusion. I can see that if the there is one electron of spin up the spectral function yields ω=E while if there is 0 ω=E+U. But how exactly is it to be interpreted?