Two-particle Green's functions in the theory of an electron gas

Eberhard K. U. Gross, E. Runge, Olle Heinonen

Part 1 Fundamentals and examples: systems of identical particles second quantization for fermions second quantization for bosons unitary transformations and field operators example - the Hamiltonian of translationally invariant systems in second quantization density operators the Hartree-Fock approximation restricted Hartree-Fock approximation and the symmetry dilemma Hartree-Fock for translationally invariant systems the homogeneous electron gas in the Hartree-Fock approximation long-range correlations in the electron-gas - plasmons phonons superconductivity. Part 2 Green's functions: pictures the single-particle Green's function and the hierarchy of equations of motion. Part 3 Perturbation theory: time-dependent perturbation theory with adiabatic turning-on of the interaction particle and hole operators and Wick's theorem Feynman diagrams diagrammatic calculation of the vacuum amplitude an example - the Gell-Mann-Brueckner correlation energy of a dense electron gas diagrammatic calculation of the single-particle Green's function - Dyson's equation diagrammatic analysis of the Green's function G(kappa, omega) self-consistent perturbation theory, higher-order Hartree-Fock theory the quasi-particle concept diagrammatic calculation of the two-particle Green's function and the polarization propagator effective interaction and dressed vertices plasmons in higher order perturbation theory at finite temperatures. Part 4 Fermi liquid theory: introduction equilibrium properties transport equation and collective modes microscopic derivation of the Landau fermi liquid theory applications to the Kondo problem.

Joachim Brand, Lorenz S. Cederbaum

Paola Gori‐Giorgi

Steven Crisostomo, Eberhard K. U. Gross, Kieron Burke

Density-functional theory (DFT) calculations yield useful ground-state energies and densities, while Green's function techniques (such as GW) are mostly used to produce spectral functions. From the Galitskii-Migdal formula, we extract the exchange correlation of DFT directly from a Green's function. This spectral representation provides an alternative to the fluctuation-dissipation theorem of DFT, identifying distinct single-particle and many-particle contributions. Results are illustrated on the uniform electron gas and the two-site Hubbard model.

Viktor Borisovich Bobrov

It has been shown with the use of the virial theorem and the equation of motion for the single-particle Green’s function that the thermodynamic properties of a single-component quantum gas beyond the perturbation theory are fully determined by the two-particle Green’s function Moscow Power Engineering Institute.

A. V. Koshelkin