The many-body Green function of degenerate systems

Abstract

A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0 leading to eigenstates of H0+V for degenerate systems. These initial states are eigenstates of P0 V P0, where P0 is the projection onto a degenerate eigenspace of H0. This result is used to give the proper definition of the Green function, the statistical Green function and the non-equilibrium Green function of degenerate systems. The convergence of these Green functions is established.

4 pages, 1 figure

References in corpus (2)

• Shell-model calculations and realistic effective interactions
• Optical to UV spectra and birefringence of SiO${}_2$ and TiO${}_2$: First-principles calculations with excitonic effects

Cited by in corpus (15)

• The self-consistent Dyson equation and self-energy functionals: failure or new opportunities?
• Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads
• First-principles calculations of the electronic structure of open-shell condensed matter systems
• Connections between many-body perturbation and coupled-cluster theories
• Quantum correlations in a cluster-like system
• Can $GW$ Handle Multireference Systems?
• Gell-Mann and Low formula for degenerate unperturbed states
• Controllability of spin-boson systems
• The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems
• Tree expansion in time-dependent perturbation theory
• Gauge invariance and relativistic effects in photon absorption and scattering by matter
• Nonequilibrium Fractional Josephson Effect
• Ensemble Green's function theory for interacting electrons with degenerate ground states
• Diagonal Padé Approximant of the one-body Green's function, a study on Hubbard rings
• On some aspects of the definition of scattering states in quantum field theory