A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method, the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. The diagrammatic linkedness and irreducibility of the self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent framework using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

One-particle many-body Green's function theory: Algebraic recursions, linked-diagram and irreducible-diagram theorems, and general-order algorithms

254th National Meeting (2017)

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