I believe that one of the most important concepts in quantum many-body physics is that of quasi-particles and the associated incoherent excitations. Often the one particle spectral function can be written in the form.
where the first term is a well-defined peak associated with quasi-particles and total spectral weight Z_k.
The second term describes incoherent excitations, i.e., it has a weak dependence on the momentum k and as a function of omega is a broad distribution, in contrast to the sharp quasi-particle peak.
Futhermore, due to a sum rule [conservation of particle number] the total spectral weight of the incoherent part is 1-Z_k.
I think this equation is one of the most profound and important results in quantum many-body theory.
Some of this is illustrated in the figure below taken from a Nature Physics commentary by Nandini Trivedi.
I have two historical questions I am struggling to find answers for:
1. When and by whom was the equation above first clearly written down and elucidated?
I suspect sometime in the 1950-60s by Landau, Pines, Nozieres, Kadanoff, Baym, or Hubbard?
I looked in AGD and several other old books but could not find it.
2. When was the first time that the incoherent part of the spectral function was definitively observed in
By this I don't mean just seeing some background [that could be noise], but actually showing that the incoherent background has the weight 1-Z_k. I presume an ARPES experiment in the past two decades.
I should know this, but just can't quickly find the answer.