✍ Scribed by Roger Balian; Cyrano De Dominicis
No coin nor oath required. For personal study only.
Some analytical properties of the mass operator are examined in perturbation theory, and a simple form of the one particle Green's function for a grand canonical ensemble is ob ta in ed by analytical continuati on . An approxima.tion is then considered, which neglects terms where energy denomin a t ors are accidentally vanishing or equal. In this approximation, all qua nt ities of interest can be diagrammatically built up like the corresponding ones for the ground state of a system of N particles ; on ly the st atisti cal fa ctors for each state are no longer step functions in momen tum space. The resu lting expressio ns for " local " vidal coefficien ts are ex am ined. also th e en ergy of the system fi ts in with the form Landau ha s ass umed for his th eory of Fermi liquids. In sp ite of difficulties arising from th e us e of a d iscrete sp ectrum of energies, this approximation is suggestive of what a more exact treatment cou ld be.
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