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An infinite volume expansion for many fermion Green’s functions. (English) Zbl 0921.35140
Summary: We prove the convergence of a simplified cluster/Mayer expansion at one energy scale for three-space-time-dimensional many-fermion systems. The bounds are uniform in the scale. We iterate them to show that the sum of all diagrams that contain no two- or four-legged subdiagrams converges. Our results are suited to a multiscale construction of the full system.

35Q40 PDEs in connection with quantum mechanics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81V70 Many-body theory; quantum Hall effect
81T18 Feynman diagrams