Perturbation expansion of the single-particle propagator

Albert Schmid

Willem H Dickhoff, Dimitri Van Neck

Identical Particles Second Quantization Independent-Particle Model for Fermions in Finite Systems Two-Particle States and Interactions Noninteracting Bosons and Fermions Propagators in One-Particle Quantum Mechanics Single-Particle Propagator in Many-Particle Systems Perturbation Expansion of the Single-Particle Propagator Dyson Equation and Self-consistent Green's Functions Mean-Field or Hartree-Fock Approximation Beyond the Mean-Field Approximation Interacting Boson Systems Excited States in Finite Systems Excited States in Infinite Systems Excited States in N 2 Systems and In-Medium Scattering Dynamical Treatment of the Self-energy in Infinite Systems Dynamical Treatment of the Self-energy in Finite Systems Bogoliubov Perturbation Expansion for the Bose Gas Boson Perturbation Theory Applied to Physical Systems In-Medium Interaction and Scattering of Dressed Particles Conserving Approximations and Excited States Pairing Phenomena Propagator Framework for Phenomenological Description of Many-Body Systems Finite Temperature Formalism and Applications.

J. Schirmer, Andreas Barth

John M. Herbert

For a system of indistinguishable fermions with pairwise interactions, we consider renormalized, perturbative expansions for the three- and four-particle propagators (Green's functions) in terms of exact one-particle propagators, along with a pair interaction that may be bare (as it appears in the Hamiltonian) or dressed (polarized). Care is taken to provide a rigorous foundation for the diagrammatic representations of these perturbation series; in particular, it is demonstrated how each topologically distinct diagram represents an embedding (in three-dimensional space) of numerous separate terms in the perturbation series. Within a renormalized ladder approximation for the three- and four-particle propagators, we derive diagram weights (which differ from the two-particle diagram weights) in order to limit the perturbation series to topologically distinct, permutationally independent diagrams. These results lay the foundation for perturbative approximations that decouple the propagator and density matrix equations of motion.