How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, for the photon Green function, for the phonon Green function)? Explanations and references for actual constructions would be greatly appreciated.
What is the use of skeleton diagrams in qft and in many-body physics?
Skeleton diagrams are usually used to discuss general properties of the perturbation series in field theory. They help to prove renormalizability of a theory, or to prove properties of correlation functions. However, they are not used in general for explicit calculation. (The main counter example is the Diagramatic Monte Carlo, that tries to compute high order of skeleton diagram series by doing Monte Carlo sampling of the diagrams.)
For example, Gavoret and Noziere (1964) used skeleton diagrams to find the exact low energy behavior of the propagator of bosonic condensates.
For a (quick) discussion of these diagrams, see for example Quantum Field Theory by Lewis H. Ryder (around p.350).
